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  • Articles  (8,313)
  • Institute of Physics  (6,031)
  • American Institute of Physics (AIP)  (2,282)
  • 2020-2024  (28)
  • 2020-2023
  • 1990-1994  (8,285)
  • Mathematics  (8,155)
  • Energy, Environment Protection, Nuclear Power Engineering  (158)
  • Natural Sciences in General
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  • Articles  (8,313)
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  • 1
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    Fermionic systems for quantum information people (2021)
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    Publication Date: 2021-10-01
    Description: The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan–Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.
    Print ISSN: 1751-8113
    Electronic ISSN: 1751-8121
    Topics: Mathematics , Physics
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  • 2
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    Towards reducing inter-city economic inequality embedded in China's Environmental Protection Tax Law (2021)
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    Publication Date: 2021-10-29
    Description: Cities are at the front line of combating environmental pollution and climate change, thus support from cities is crucial for successful enforcement of environmental policy. To mitigate environmental problems, China introduced at provincial level the Environmental Protection Tax Law in 2018. Yet the resulting economic burden on households in different cities with significantly different affluence levels remains unknown. The extent of the economic impacts is likely to affect cities’ support and public acceptability. This study quantifies the economic burden of urban households from taxation of fine particle pollution (PM2.5) for 200 cities nationwide from a “consumer” perspective, accounting for PM2.5 and precursor emissions along the national supply chain. Calculations are based on a Multi-Regional Input-Output (MRIO) analysis, the official tax calculation method and urban household consumption data from China’s statistical yearbooks. We find that the current taxation method intensifies economic inequality between cities nationally and within each province, with some of the richest cities having lower tax intensities than some of the poorest. This is due to the fact that taxes are collected based on tax rates of producing regions rather than consuming regions, that cities with very different affluence levels within a province bear the same tax rate, and that emission intensities in several less affluent cities are relatively high. If the tax could be levied based on tax rates of each city where the consumer lives, with tax rates determined based on cities’ affluence levels and with tax revenues used to support emission control, inter-city economic inequality could be reduced. Our work provides quantitative evidence to improve the environmental tax and can serve as the knowledge base for coordinated inter-city policy.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 3
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    Quantitative signal subspace imaging (2021)
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    Publication Date: 2021-10-29
    Description: We develop and analyze a quantitative signal subspace imaging method for single-frequency array imaging. This method is an extension to MUSIC (multiple signal classification) which uses (i) the noise subspace to determine the location and support of targets, and (ii) the signal subspace to recover quantitative information about the targets. For point targets, we are able to recover the complex reflectivity and for an extended target under the Born approximation, we are able to recover a scalar quantity that is related to the product of the volume and relative dielectric permittivity of the target. Our resolution analysis for a point target demonstrates this method is capable of achieving exact recovery of the complex reflectivity at subwavelength resolution. Additionally, this resolution analysis shows that noise in the data effectively acts as a regularization to the imaging functional resulting in a method that is surprisingly more robust and effective with noise than without noise.
    Print ISSN: 0266-5611
    Electronic ISSN: 1361-6420
    Topics: Mathematics , Physics
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  • 4
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    Comment on ‘Unintentional unfairness when applying new greenhouse gas emissions metrics at country level’ (2021)
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    Publication Date: 2021-06-01
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 5
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    On the relation between visual quality and landscape characteristics: a case study application to the waterfront linear parks in Shenyang, China (2021)
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    Publication Date: 2021-10-29
    Description: In recent years, Chinese cities have begun to pay attention to their rivers, and a large number of waterfront linear parks have been built in the riverside areas, so that the public can easily enjoy their landscape and entertainment functions. In this study, the visual quality of the waterfront trails and the greenbelt trails in the Waterfront linear Park around the Hunhe river in Shenyang was evaluated the basis of the Scenic Beauty Estimation Method and Semantic Differential Method, and the principal components of the landscape characteristics were extracted and a regression model of the visual quality and the landscape characteristics was established. Results show that the natural feature and the formal feature have a positive influence on the visual quality in waterfront linear parks, and the man-made feature has a negative impact on the visual quality. The six landscape characteristics are Sense of seclusion, ecology, intactness, uniqueness, unity and vitality, which are the main factors which affect the visual quality. This study puts forward improvement measures for the waterfront trails and the greenbelt trails, and the results can be applied to the planning, construction, and management of waterfront linear parks.
    Electronic ISSN: 2515-7620
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 6
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    A systematic review of life cycle assessment of hydrogen for road transport use (2021)
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    Publication Date: 2021-10-29
    Description: This study conducted a systematic literature review of the technical aspects and methodological choices in life cycle assessment (LCA) studies of using hydrogen for road transport. More than 70 scientific papers published during 2000–2021 were reviewed, in which more than 350 case studies of use of hydrogen in the automotive sector were found. Only some studies used hybrid LCA and energetic input-output LCA, whereas most studies addressed attributional process-based LCA. A categorization based on the life cycle scope distinguished case studies that addressed the well-to-tank (WTT), well-to-wheel (WTW), and complete life cycle approaches. Furthermore, based on the hydrogen production process, these case studies were classified into four categories: thermochemical, electrochemical, thermal-electrochemical, and biochemical. Moreover, based on the hydrogen production site, the case studies were classified as centralized, on-site, and on-board. The fuel cell vehicle passenger car was the most commonly used vehicle. The functional unit for the WTT studies was mostly mass or energy, and vehicle distance for the WTW and complete life cycle studies. Global warming potential (GWP) and energy consumption were the most influential categories. Apart from the GREET (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation) model and the Intergovernmental Panel on Climate Change for assessing the GWP, the Centrum voor Milieukunde Leiden method was most widely used in other impact categories. Most of the articles under review were comparative LCA studies on different hydrogen pathways and powertrains. The findings provide baseline data not only for large-scale applications, but also for improving the efficiency of hydrogen use in road transport.
    Electronic ISSN: 2516-1083
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Physics , Technology
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  • 7
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    Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad-hoc misfit functional (2021)
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    Publication Date: 2021-10-29
    Description: We address the stability issue in Calderón’s problem for a special class of anisotropic conductivities of the form σ=γA in a Lipschitz domain Ω⊆R, n≧3, when A is a known Lipschitz continuous matrix-valued function and γ is the unknown piecewise affine scalar function on a given partition of Ω. We define an ad-hoc misfit functional encoding our data and establish estimates for this class of anisotropic conductivities in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.
    Print ISSN: 0266-5611
    Electronic ISSN: 1361-6420
    Topics: Mathematics , Physics
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  • 8
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    Using deep learning to predict the East Asian summer monsoon (2021)
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    Publication Date: 2021-10-29
    Description: Accurate prediction of the East Asian summer monsoon (EASM) is beneficial to billions of people’s production and lives. Here convolutional neural networks (CNN) and transfer learning are used for predicting the EASM. The results of the constructed CNN regression model show that the prediction of the CNN regression model is highly consistent with the reanalysis dataset, with correlation coefficient of 0.78, which is higher than that of each of the current state-of-the-art dynamic models. The heat map method indicates that the robust precursor signals in the CNN regression model agree well with previous theoretical studies, and can provide the quantitative contribution of different signals for EASM prediction. The CNN regression model can predict the EASM one year ahead with a confidence level above 95%. The above method can not only improve the prediction of the EASM but also help to identify the involved physical predictors.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 9
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    Reply to Comment on ‘Unintentional unfairness when applying new greenhouse gas emissions metrics at country level’ (2021)
    Institute of Physics
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    Publication Date: 2021-06-01
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 10
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    Current status of eye-lens dosimetry in Canada (2021)
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    Publication Date: 2021-10-29
    Print ISSN: 0952-4746
    Electronic ISSN: 1361-6498
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 11
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    Spatial priorities for biodiversity and ecosystem services considering theoretical decision-makers' attitudes to risk (2021)
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    Publication Date: 2021-10-29
    Description: Choosing appropriate spatial priorities for protected areas (PAs) to conserve ecosystem services (ESs) and biodiversity is a challenge for decision-makers under limited land resources, especially when facing uncertain protection consequences or conflicting protection objectives. Attitudes toward risk will influence actions, which will, in turn, impact consequences. To understand how theoretical decision-maker attitudes towards risk impact protection effectiveness for biodiversity and ESs (e.g., water retention, soil retention, flood mitigation, water purification and carbon sequestration) and how this information can be integrated into effective PAs management, we examined Hainan Island as a case study. We used the ordered weighted averaging algorithm to assess the impact of attitude towards risk in PA management. Decision-makers’ attitude towards risk scenarios (from risk-averse and risk-taking) showed higher mean protection effectiveness (2.41–2.85) than existing PAs (2.37), indicating that there is still room for improvement in biodiversity and ESs conservation in existing PAs. In addition, among the seven examined risk scenarios, the higher risk aversion scenario showed the best outcome. In comparison to existing PAs, this scenario improved mean protection effectiveness (20.13%) as well as the protection effectiveness of water retention (24.84%), water purification (11.46%), flood mitigation (8.84%), soil retention (16.63%), carbon sequestration (5.31%), and biodiversity (12.84%). Thus, our research shows that the influence of theoretical decision-makers’ attitudes towards risk could be considered by OWA method which could provide a normative model of what the right choice given theoretical risk attitudes is while selecting priority area for biodiversity and ESs.
    Electronic ISSN: 2515-7620
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 12
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    A clustering approach to improve spatial representation in water-energy-food models (2021)
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    Publication Date: 2021-10-29
    Description: Currently available water-energy-food (WEF) modelling frameworks to analyse cross-sectoral interactions often share one or more of the following gaps: (a) lack of integration between sectors, (b) coarse spatial representation, and (c) lack of reproducible methods of nexus assessment. In this paper, we present a novel clustering tool as an expansion to the Climate-Land-Energy-Water-Systems modelling framework used to quantify inter-sectoral linkages between water, energy, and food systems. The clustering tool uses Agglomerative Hierarchical clustering to aggregate spatial data related to the land and water sectors. Using clusters of aggregated data reconciles the need for a spatially resolved representation of the land-use and water sectors with the computational and data requirements to efficiently solve such a model. The aggregated clusters, combined together with energy system components, form an integrated resource planning structure. The modelling framework is underpinned by an open-source energy system modelling tool—OSeMOSYS—and uses publicly available data with global coverage. By doing so, the modelling framework allows for reproducible WEF nexus assessments. The approach is used to explore the inter-sectoral linkages between the energy, land-use, and water sectors of Viet Nam out to 2030. A validation of the clustering approach confirms that underlying trends actual crop yield data are preserved in the resultant clusters. Finally, changes in cultivated area of selected crops are observed and differences in levels of crop migration are identified.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 13
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    The world’s largest heliothermal lake newly formed in the Aral Sea basin (2021)
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    Publication Date: 2021-10-29
    Description: The Aral Sea desiccation is one of the worst aquatic ecological disasters of the last century, important for understanding the worldwide trends to degradation of arid lakes under water use and climate change. Formerly the fourth largest lake worldwide, the Aral Sea has lost ∼90% of its water since the early 1960s due to irrigation in its drainage basin. Our survey on the seasonal thermal and mixing regime in Chernyshev—a semi-isolated hypersaline part of the Aral Sea—revealed a newly formed two-layered structure with strong gradients of salinity and water transparency at mid-depths. As a result, the Chernyshev effectively accumulates solar energy, creating a temperature maximum at the water depth of ∼5 m with temperatures up to 37 °C. Herewith, this part of the Aral Sea has evolved to an unprecedently large (∼80 km2) heliothermal lake akin to artificial solar ponds used for ‘green energy’ production. The newly formed heliothermal lake, with transparent and freshened layer on top of the hypersaline and nutrient-rich deep water, acts as a solar energy trap and facilitates intense biogeochemical processes. The latter reveal themselves in practically 100% opacity of the deep layer to the solar light, permanent deep anoxia, and growing methane concentrations. The recent emergence of the Chernyshev as a heliothermal lake provides an opportunity for tracing the biogeochemical and ecological response of aquatic ecosystems to suddenly changed environmental conditions.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 14
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    Efficient pathways to zero-carbon energy use by water supply utilities: an example from London, UK (2021)
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    Publication Date: 2021-10-01
    Description: Urban water utilities are increasing their use of energy-intensive technologies such as desalination and long-distanced pumped transfers. Under pressure to reduce their energy-related carbon emissions to zero, water utilities have devised a variety of energy management strategies, including the purchase of renewable energy and self-generation of electricity using locally installed renewables. These strategies will incur different costs for the utility, whilst some may have implications for the reliability of water supply systems. Yet the trade-offs between costs, water security and energy sustainability remain unexplored. Here, we present a regional scale analysis to test competing energy strategies, mapping pathways to zero carbon energy and water security. Results from a case-study of the London water system show a balanced approach that allows for some energy self-generation, using biogas, solar and wind, while also purchasing green energy credits from the electricity supply grid can best navigate this trade-off. Balanced investment plans can accommodate energy-intensive water supply techniques such as long-distance transfers, desalination and effluent reuse while meeting energy targets. By becoming energy generators and also adopting more flexible arrangements for energy use, water utilities could become significant players in energy markets.
    Print ISSN: 1748-9318
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 15
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    Multipoint formulae for inverse scattering at high energies (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 16
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    Igor’ Moiseevich Krichever (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 17
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    Tetrahedron equation: algebra, topology, and integrability (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 18
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    Groups generated by involutions, numberings of posets, and central measures (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 19
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    Multilevel interpolation for Nikishin systems and boundedness of Jacobi matrices on binary trees (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 20
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    Chaos and integrability in -geometry (2021)
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    Publication Date: 2021-08-01
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    Topics: Mathematics
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  • 21
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    Dynamical Bethe algebra and functions on pairs of quasi-polynomials (2021)
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    Publication Date: 2021-08-01
    Print ISSN: 0036-0279
    Electronic ISSN: 1468-4829
    Topics: Mathematics
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  • 22
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    Checkered landscapes: hydrologic and biogeochemical nitrogen legacies along the river continuum (2021)
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    Publication Date: 2021-10-27
    Description: Decades of agricultural intensification have led to elevated stream nitrogen (N) concentrations and eutrophication of inland and coastal waters. Despite widespread implementation of a range of strategies to reduce N export, expected improvements in water quality have not been observed. This lack of success has often been attributed to the existence of legacy N stores within the landscape. Here, we use the ELEMeNT-N model to quantify legacy accumulation and depletion dynamics over the last century (1930–2016) across 14 nested basins within the Grand River Watershed, a 6800 km2 agricultural watershed in the Lake Erie Basin. Model results reveal significant legacy N accumulation across the basin, ranging from 705 to 1071 kg ha−1, creating a checkered landscape of N legacies. The largest proportion (82%–96%) of this accumulated N is stored in soil organic N reservoirs, as biogeochemical legacy, and the remaining in groundwater, as hydrologic legacy. The fraction of N surplus accumulated in soil and groundwater is most strongly correlated with the calibrated watershed mean travel time µ, with the accumulation increasing with increases in µ. The mean travel time ranges from 5 to 34 years across the watersheds studied, and increases with increase in tile drainage, highlighting the strong control of anthropogenic management on legacy accumulation. Water quality improvement timescales were found to be heterogeneous across the watersheds, with greater legacies contributing to slower recovery.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 23
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    Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves (2021)
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    Publication Date: 2021-08-01
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  • 24
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    Nutrient-extended input–output (NutrIO) method for the food nitrogen footprint (2021)
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    Publication Date: 2021-10-29
    Description: Agro-food systems require nutrient input from several sources to provide food products and food-related services. Many of the nutrients are lost to the environment during supply chains, potentially threatening human and ecosystem health. Countries therefore need to reduce their nutrient/nitrogen footprints. These footprints are importantly affected by links between sectors. However, existing assessments omit the links between sectors, especially between the agriculture, manufacturing, and energy sectors. We propose a novel approach called the nutrient-extended input–output (NutrIO) method to determine the nutrient footprint as a sum of direct and indirect inputs throughout the supply chains from different sources of nutrients. The NutrIO method is based on a nutrient-based material flow analysis linked to economic transactions. Applying this method, we estimated the nitrogen footprint of Japan in 2011 at 21.8 kg-N capita−1yr−1: 9.7 kg-N capita−1 yr−1 sourced from new nitrogen for agriculture and fisheries, 7.0 kg-N capita−1 yr−1 from recycled nitrogen as organic fertilizers, and 5.1 kg-N capita−1 yr−1 from industrial nitrogen for chemical industries other than fertilizers. A further annexed 55.4 kg-N capita−1 yr−1 of unintended nitrogen input was sourced from fossil fuels for energy production. The nitrogen intensity of the wheat and barley cultivation sector, at 1.50 kg-N per thousand Japanese yen (JPY) production, was much higher than that of the 0.12 kg-N per thousand JPY production for the rice cultivation sector. Industrial nitrogen accounted for 2%–7% of the nitrogen footprint of each major food-related sector. The NutrIO nitrogen footprint sourced from new nitrogen for agriculture and fisheries, at 8.6 kg-N capita−1 yr−1 for domestic final products, is comparable to the food nitrogen footprint calculated by other methods, at 8.5–10.5 kg-N capita−1 yr−1. The NutrIO method provides quantitative insights for all stakeholders of food consumption and production to improve the nutrient use efficiencies of agro-food supply chains.
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  • 25
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    Predicting hotspots for invasive species introduction in Europe (2021)
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    Publication Date: 2021-10-29
    Description: Plant pest invasions cost billions of Euros each year in Europe. Prediction of likely places of pest introduction could greatly help focus efforts on prevention and control and thus reduce societal costs of pest invasions. Here, we test whether generic data-driven risk maps of pest introduction, valid for multiple species and produced by machine learning methods, could supplement the costly species-specific risk analyses currently conducted by governmental agencies. An elastic-net algorithm was trained on a dataset covering 243 invasive species to map risk of new introductions in Europe as a function of climate, soils, water, and anthropogenic factors. Results revealed that the BeNeLux states, Northern Italy, the Northern Balkans, and the United Kingdom, and areas around container ports such as Antwerp, London, Rijeka, and Saint Petersburg were at higher risk of introductions. Our analysis shows that machine learning can produce hotspot maps for pest introductions with a high predictive accuracy, but that systematically collected data on species’ presences and absences are required to further validate and improve these maps.
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  • 26
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    Projected changes in seasonal and extreme summertime temperature and precipitation in India in response to COVID-19 recovery emissions scenarios (2021)
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    Publication Date: 2021-10-29
    Description: Fossil fuel and aerosol emissions have played important roles on climate over the Indian subcontinent over the last century. As the world transitions toward decarbonization in the next few decades, emissions pathways could have major impacts on India’s climate and people. Pathways for future emissions are highly uncertain, particularly at present as countries recover from COVID-19. This paper explores a multimodel ensemble of Earth system models leveraging potential global emissions pathways following COVID-19 and the consequences for India’s summertime (June–July–August–September) climate in the near- and long-term. We investigate specifically scenarios which envisage a fossil-based recovery, a strong renewable-based recovery and a moderate scenario in between the two. We find that near-term climate changes are dominated by natural climate variability, and thus likely independent of the emissions pathway. By 2050, pathway-induced spatial patterns in the seasonally-aggregated precipitation become clearer with a slight drying in the fossil-based scenario and wetting in the strong renewable scenario. Additionally, extreme temperature and precipitation events in India are expected to increase in magnitude and frequency regardless of the emissions scenario, though the spatial patterns of these changes as well as the extent of the change are pathway dependent. This study provides an important discussion on the impacts of emissions recover pathways following COVID-19 on India, a nation which is likely to be particularly susceptible to climate change over the coming decades.
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
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  • 27
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    Influence of high road labor policies and practices on renewable energy costs, decarbonization pathways, and labor outcomes (2021)
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    Publication Date: 2021-10-29
    Description: Achieving an economy-wide net-zero greenhouse gas emissions goal by mid-century in the United States entails transforming the energy workforce. In this study, we focus on the influence of increased labor compensation and domestic manufacturing shares on (1) renewable energy technology costs, (2) the costs of transitioning the U.S. economy to net-zero emissions, and (3) labor outcomes, including total employment and wage benefits, associated with the deployment of utility-scale solar photovoltaics (PV) and land based and offshore wind power. We find that manufacturing and installation labor cost premiums as well as increases in domestic content shares across wind and utility-scale solar photovoltatic supply chains result in relatively modest increases in total capital and operating costs. These small increases in technology costs may be partially or fully offset by increases in labor productivity. We also show that solar and wind technology cost premiums associated with high road labor policies have a minimal effect on the pace and scale of renewable energy deployment and the total cost of transitioning to a net-zero emissions economy. Public policies such as tax credits, workforce development support, and other instruments can redistribute technology cost premiums associated with high road labor policies to support both firms and workers.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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    Human arsenic exposure risk via crop consumption and global trade from groundwater-irrigated areas (2021)
    Institute of Physics
    Details
    Publication Date: 2021-10-29
    Description: While drinking water is known to create significant health risk in arsenic hazard areas, the role of exposure to arsenic through food intake is less well understood, including the impact of food trade. Using the best available datasets on crop production, irrigation, groundwater arsenic hazard, and international crop trade flows, we estimate that globally 17.2% of irrigated harvested area (or 45.2 million hectares) of 42 main crops are grown in arsenic hazard areas, contributing 19.7% of total irrigated crop production, or 418 million metric tons (MMT) per year of these crops by mass. Two-thirds of this area is dedicated to the major staple crops of rice, wheat, and maize (RWM) and produces 158 MMT per year of RWM, which is 8.0% of the total RWM production and 18% of irrigated production. More than 25% of RWM consumed in the South Asian countries of India, Pakistan, and Bangladesh, where both arsenic hazard and degree of groundwater irrigation are high, originate from arsenic hazard areas. Exposure to arsenic risk from crops also comes from international trade, with 10.6% of rice, 2.4% of wheat, and 4.1% of maize trade flows coming from production in hazard areas. Trade plays a critical role in redistributing risk, with the greatest exposure risk borne by countries with a high dependence on food imports, particularly in the Middle East and small island nations for which all arsenic risk in crops is imported. Intensifying climate variability and population growth may increase reliance on groundwater irrigation, including in arsenic hazard areas. Results show that RWM harvested area could increase by 54.1 million hectares (179% increase over current risk area), predominantly in South and Southeast Asia. This calls for the need to better understand the relative risk of arsenic exposure through food intake, considering the influence of growing trade and increased groundwater reliance for crop production.
    Print ISSN: 1748-9318
    Electronic ISSN: 1748-9326
    Topics: Energy, Environment Protection, Nuclear Power Engineering
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    Compilation of two-point and four-point graphs in field theory in noninteger dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3866-3880 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: Two-point and four-point graphs appearing in a three-loop approximation in the field theory renormalization group scheme are calculated in general dimensions. Combining Feynman parameterization and direct integration loop integrals are represented in the form of the expressions, depending on the space dimension d as a parameter. The expressions obtained enables one to consider renormalization group functions directly at noninteger d.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530452
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    A connection between quantum dynamics and approximation of Markov diffusions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4505-4516 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: It is observed that the existence of an attracting set in the class of solutions to the stochastic Lagrangian variational principle leads to a natural problem of convergence of diffusions in the Carlen class. It is then shown how dynamical properties enable one to prove some convergence results in the two-dimensional Gaussian case.
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    Invariants of Lagrangians and their classifications (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4568-4593 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: A complete classification of natural transformations of finite order of Lagrangians into energies over n-dimensional manifolds, where n≥2, is given herein. The classification of natural transformations of finite order of vector fields and Lagrangians into energies and constants of the motion is also obtained for n≥3. By using these results, a classification of Lagrangians into Poincaré–Cartan one-forms and Legendre transformations is obtained.
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    Dirac's equation on the quantum net (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3936-3958 
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    ISSN: 1089-7658
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    Notes: The quantum net model differs from other quantizations and discretizations of space-time in being founded upon quantum-logical principles. Fermions are envisaged as arising from defects in the net. Such defects are investigated and it is found that the attempt to vary them infinitesimally gives rise to a reticular version of the Dirac operator, which now has a simple interpretation in terms of quantum mechanical infinitesimal parallel transport. The analog of the usual massless Weyl equations are found to hold on the net, and algebraic solutions are deduced by exploiting its inherent logical structure. A correspondence principle then applies to show that these equations and their solutions correspond precisely to the ones expected in the continuum. (In the course of this, new basis-independent expressions for the complex Minkowski-space Dirac matrices are found.) Finally, an attempt is made to introduce gravity into the net, and the flat space Dirac Lagrangian is modified accordingly.
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    The exact solutions of the equation for a composite particle in the external electromagnetic fields (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4497-4504 
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    ISSN: 1089-7658
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    Notes: Exact analytic solutions are provided for a class of equations describing a composite scalar particle in constant electric and magnetic fields, and also in plane electromagnetic fields. The external fields are taken in both classical and quantum cases. A detailed physical analysis of the results is given.
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    Knowledge about noncommuting quantum observables by means of Einstein–Podolsky–Rosen correlations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4534-4546 
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    Notes: It is well known that quantum physics forbids the simultaneous measurement of two noncommuting projection operators. However, sometimes there exists a third projection (mirror projection) which may be measured together with the second one and whose outcomes are completely correlated, in the Einstein–Podolsky–Rosen sense, with the outcomes of the first projection. In this article the states for which such a mirror projection exists are characterized and a procedure for constructing the mirror is given. In particular, it is shown that for two noncommuting projections there are always states for which the mirror projection exists, but also states for which it does not exist.
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    Existence theorems for 90° vortex–vortex scattering (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4651-4660 
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    Notes: A Cauchy problem is formulated with data that describe the scattering of two vortices in a superconductor, and the following is proven: First, a unique global finite-energy solution exists. Second, the symmetry of the solution rules out all cases other than 0°, 90°, or 180° scattering. Third, a local analytic solution exists near the origin. The leading terms of this solution show that, of the three cases, 90° scattering is realized.
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    A Bäcklund transformation and nonlinear superposition formula of a modified Korteweg–de Vries-type bilinear equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4739-4745 
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    Notes: A modified Korteweg–de Vries (mKdV)-type bilinear equation that has been shown to pass the three-soliton solution and the Painlevé tests [see, J. Math. Phys. 2094, 28 (1987); 2572, 31 (1990)] is considered herein. In this article, a Bäcklund transformation and a nonlinear superposition formula are proven rigorously. As an application of the obtained results, N-soliton solutions are obtained. Therefore, the integrability of this mKdV-type bilinear equation is confirmed.
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    The potential constraints of the KP system and the corresponding Hamiltonian equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4725-4738 
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    Notes: In this paper all the potential constraints (with or without first-order partial derivatives) of the KP system, from which the associated linear problem can be restricted into a (1+1)-dimensional Hamiltonian equation, are obtained by using the sufficient and necessary condition for a nonlinear equation to be a Hamiltonian system. Some well-known integrable systems, such as (1+1)-dimensional AKNS system, generalized NS system, and several new Hamiltonian equations, are deduced as particular examples.
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    Soliton solutions and gauge equivalence for the quadratic bundle (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4799-4808 
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    Notes: A more simple form than the one given by Vaklev [J. Math. Phys. 33, 4111 (1992)] for the soliton solutions related to the quadratic bundle [E. A. Kuznetzov and A. V. Mikhailov, Teor. Mat. Fiz. 30, 303 (1977); D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978); V. S. Gerdjikov, M. I. Ivanov, and P. P. Kulish, Teor. Mat. Fiz. 44, 342 (1980); V. S. Gerdjikov and M. I. Ivanov, Bulg. J. Phys. 10, 13 (1983); 10, 2, 129 (1983)] is obtained. The corresponding solutions for the gauge equivalent case are obtained as well. Among them one can find the N-soliton solutions for the derivative nonlinear Schrödinger equation, their gauge equivalents, etc. The method used in the article allows one to express some integrals by means of appropriate determinants and thus the result is obtained without integration.
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    Total mass-momentum of arbitrary initial-data sets in general relativity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4157-4177 
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    Notes: For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of "asymptotic spinors.'' A generalization to an arbitrary initial-data set is obtained. The mass-momentum is retained as a Hermitian quadratic form, but the space of "asymptotic spinors'' on which it is a function is modified. Indeed, the dimension of this space may range from zero to infinity, depending on the initial data. There is given a variety of examples and general properties of this generalized mass-momentum.
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    Spectral functions and zeta functions in hyperbolic spaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4217-4246 
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    Notes: The spectral function (also known as the Plancherel measure), which gives the spectral distribution of the eigenvalues of the Laplace–Beltrami operator, is calculated for a field of arbitrary integer spin (i.e., for a symmetric traceless and divergence-free tensor field) on the N-dimensional real hyperbolic space (HN). In odd dimensions the spectral function μ(λ) is analytic in the complex λ plane, while in even dimensions it is a meromorphic function with simple poles on the imaginary axis, as in the scalar case. For N even a simple relation between the residues of μ(λ) at these poles and the (discrete) degeneracies of the Laplacian on the N sphere (SN) is established. A similar relation between μ(λ) at discrete imaginary values of λ and the degeneracies on SN is found to hold for N odd. These relations are generalizations of known results for the scalar field. The zeta functions for fields of integer spin on HN are written down. Then a relation between the integer-spin zeta functions on HN and SN is obtained. Applications of the zeta functions presented here to quantum field theory of integer spin in anti-de Sitter space–time are pointed out.
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    The q-gamma, q-beta functions, and q-multiplication formula (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4268-4276 
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    Notes: In this article the q-deformed gamma function and q-deformed beta function are discussed in detail. Three definitions for the q-gamma function are obtained and the q-deformed duplication and multiplication formulas are proven. The q-beta function is defined and its useful properties are derived.
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    Topological entropy for appropriately approximated C*-algebrasa) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4303-4333 
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    Notes: "Classical'' topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author's recent development of a noncommutative generalization of topological entropy, in the natural setting of general C*-algebras as the noncommutative counterpart of continuous function algebras on compact spaces, is presented in a slightly modified and improved form. This includes both a survey of earlier results with some important corrections, and also new general results in response to (and inspired by) a more recent counterproposal for a noncommutative topological entropy by Thomsen. Finally, some partially new examples for the calculation of the defined topological entropy are shown. The rather self-evident physical interpretation in the framework of (operator-algebraic) quantum statistical mechanics and of "chaotic'' quantum dynamical systems is briefly touched upon.
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    Adjoint boson realization of SU(N) and a family of structural zeros of 6j coefficients (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4383-4390 
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    Notes: For the fundamental boson realization of SU(N) in its principal SO(3) basis, the generators of SU(N) are SO(3) tensor operators constructed out of one single type of boson, namely a boson with SO(3) multiplet label (N−1)/2. Here, the adjoint boson realization of SU(N) is given: this time the SO(3) tensor operators are constructed by means of N−1 types of bosons [those with SO(3) labels 1,2,..., N−1]. The validity of this realization depends upon a new identity between 6j coefficients. From this realization, or equivalently from this new identity, one can deduce the existence of a family of structural zeros of 6j coefficients.
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    Nonstandard scalar quantum fields (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3817-3844 
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    Notes: This article presents a theory of scalar quantum fields based on nonstandard analysis. Free scalar momentum fields and free Klein–Gordon fields are treated first. It is shown that the nonrigorous formalism of the standard theory can be replaced by a mathematically rigorous nonstandard theory. The second quantized energy–momentum operators are derived and the free quantum fields are diagonalized. Interacting scalar fields are considered and a nonstandard scattering operator is derived. A nonstandard counterpart to Wick's theorem is developed and the φ4 interaction is briefly discussed.
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    Precise exponential estimates in adiabatic theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3889-3915 
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    Notes: General adiabatic evolutions associated to Hamiltonians, which admit a holomorphic extension with respect to the time variable in a complex strip, and whose spectrum satisfies a gap condition are studied. An explicit rate of exponential decay is given, which is related to simple geometric quantities associated to the spectrum of the Hamiltonian, for the transition probability between the two parts of the spectrum when the evolution is taken from −∞ to +∞.
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    Phase space structure of non-Abelian Chern–Simmons particles (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3959-3968 
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    Notes: The classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles is investigated by first constructing the product space of associated SU(n+1) bundle with CPn as the fiber. The Poisson bracket is calculated using the symplectic structure on the associated bundle and it is found that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, a direct product of the associated bundle is taken by the space of all connections and a specific connection is chosen by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Lee and Oh [Phys. Rev. Lett. 72, 1141 (1994)].
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    Isotropic classical spin chains showing nearest neighbor correlated cationic distributions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3998-4004 
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    Notes: A model is proposed for calculating the magnetic susceptibility of isotropic classical spin chains showing nearest neighbor correlated cationic distributions. It allows one to obtain a general closed-form expression: This expression formally looks like previous ones obtained in the case of random chains for which the neighboring cationic species are not correlated; but here the previous intervening scalar parameters are replaced by vectorial and matricial expressions.
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    Lattice solitons directly by the bilinear method (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4057-4066 
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    Notes: Recently a doubly periodic solution of the Kadomtsev–Petviashvili equation was deduced by summing over component solitons. The same solution was derived directly by the Hirota bilinear method. This alternate route enables one to obtain a new solution. Such a mechanism can also be applied to wavepacket dynamics, e.g., the Davey–Stewartson equation.
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    Gravitational mass anomaly (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4178-4183 
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    Notes: The mass of gravitational sources differs by a factor of 2 when computed by the Komar superpotential and when computed in the gravitational weak field limit. The difference has been recognized for some time since both the linearized theory and the Einstein pseudotensor yield the same value, different by a factor of 2 from the Komar mass. The great advantage of the Komar superpotential over other methods is its tensorial formulation, however it fails to produce a Noether quantity. A different tensorial method is suggested that is free of the mass anomaly, namely, the zero and first Taub numbers [Phys. Rev. D 47, 474 (1993)] which are indeed Noether quantities. The zeroth Taub number is obtained from the Penrose–Goldberg superpotential [Phys. Rev. D 41, 410 (1990)].
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    Maximum entropy algorithm for spectral estimation problem with aipriori information (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4372-4382 
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    Notes: The power density estimation problem with a priori information about spectrum is considered. The problem is reduced to a power density estimation problem with spectral gaps. The solution of the problem is studied in the context of the trigonometric moment problem with gaps. The necessary and sufficient conditions are established for the existence of solution and all solutions are described in indeterminate cases. A new definition of the entropy functional is given. The effective algorithm to construct maximum entropy solution is proposed. A number of explicit illustrations are presented.
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    A simple difference realization of the Heisenberg q-algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3253-3260 
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    Notes: A realization of the Heisenberg q-algebra whose generators are first-order difference operators on the full real line is discussed herein. The eigenfunctions of the corresponding q-oscillator Hamiltonian are given explicitly in terms of the q−1-Hermite polynomials. The nonuniqueness of the measure for these q-oscillator states is also studied.
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    On integrable models related to the osp(1,2) Gaudin algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3261-3272 
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    Notes: The osp(1,2) Gaudin algebra is defined and integrable models described by it are considered. The models include the osp(1,2) Gaudin magnet and the Dicke model related to it. Detailed discussion of the simplest cases of these models is presented. The effect of the presence of fermions on the separation of variables is indicated.
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    An involutive system and integrable C. Neumann system associated with the modified Korteweg–de Vries hierarchy (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2978-2982 
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    Notes: In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.
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    Note on a solution of the algebraically special perturbation of the Schwarzschild black hole (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3025-3028 
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    Notes: An algebraically special solution of the Regge–Wheeler–Zerilli equation that has not been noticed is examined. This solution is proved to be related to Chandrasekhar's solution but has a simpler analytical expression.
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    Addendum to "The pseudodifferential operator square root of the Klein–Gordon equation'' [J. Math. Phys. 34, 3918 (1993)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3769-3769 
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    Fluctuations of a rotating impulsive wave (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3043-3050 
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    Notes: The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a "rotating'' cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is found.
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    Vector-coherent-state representations of so(5) in an so(3) basis (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3163-3177 
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    Notes: Vector coherent state theory is used to give an algorithm for constructing the so(5) irreps of type [N,0] and [N,N] in the physical so(3) basis. The construction is remarkably simple and permits the matrices of the so(5) operators, for irreps of low-dimension and/or small multiplicities, to be computed by hand. The construction is applied to the [2,0] and [2,2] irreps to illustrate the process.
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    An algorithm to calculate the invariants of any Lie algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3146-3162 
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    Notes: An analytical method to calculate invariants is developed, based on the theory of complete systems of simultaneous linear first order partial differential equations. The application of this algorithm to the general case, in which the invariants are not polynomials is included. For the case of Lie algebras with one invariant the procedure of finding the invariant can be computerized. As an example of this procedure, the algorithm is applied in the calculation of the invariants of the group SA(n,R). The explicit construction of its invariants for n=2, 3, 4 is given. A theorem determining the order of a polynomial invariant of a Lie group is proven allowing us to show that the invariant of SA(n,R) is a homogeneous polynomial of order 1/2n(n+1) in the generators. From this fact an immediate consequence is that the order in the generators of translations is n. The method is also applied in the calculation of invariants of the dimension six solvable Lie algebras, and dimension seven nilpotent.
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    Generalized supersymmetric quantum mechanics on Riemann surfaces with meromorphic superpotentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2074-2082 
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    Notes: The structure of generalized supersymmetry with mutually commuting involutions for the meromorphic supersymmetric quantum mechanics on the compact Riemann surface is introduced. For this purpose a Riemann surface is considered as a self-conjugate complex manifold. On this basis the Witten index for the new involution is calculated.
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    Supersymmetric quantum mechanics and the Korteweg–de Vries hierarchy (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2142-2156 
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    Notes: The connection between supersymmetric quantum mechanics and the Korteweg–de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the τ function by means of supersymmetric quantum mechanics is discussed.
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    A nonprincipal value prescription for the temporal gauge (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2210-2217 
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    Notes: A nonprincipal value prescription is used to define the spurious singularities of Yang–Mills theory in the temporal gauge. Typical one-loop dimensionally regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.
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    On the possibility of localized wave propagation using a classical two-fluid model of superconductors (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2233-2258 
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    Notes: In this paper, the classical two-fluid model for superconductors is used to determine the time-dependent partial differential equations (PDEs) which govern wave propagation in superconducting media. These equations are then solved exactly in both two and three dimensions using localized wave solutions rather than the traditional eigenfunction solutions. We have applied these localized wave solutions to the problem of a symmetric superconducting slab, neglecting the normally conducting current density, and found that the resultant focus wave mode magnetic field solution expels flux from the interior of the slab and can regain its initial amplitude as it travels along the surface of the slab. A comparison of the transverse part of the localized wave solution with the transverse part of the more usual plane wave solution shows remarkable agreement.
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    Dirac equation and Clifford algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2309-2314 
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    Notes: The Dirac equation is rewritten in the framework of a Clifford algebra, revealing some new features, of which the most interesting is the U(1)×SU(2) symmetry of the corresponding Lagrangian.
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    Critical exponents in the imperfect and the free Bose gas (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2357-2370 
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    Notes: The field fluctuations are studied for the free and imperfect Bose gas. In the phase where there is condensation, these field fluctuations are abnormal, with critical exponents depending on the way the symmetry-breaking external field tends to zero in the thermodynamic limit. On the critical line there is also abnormal behavior, but the dependence on the way the field disappears, is slightly different. For densities below the critical density, the fluctuations are normal and independent of the way the external field goes to zero.
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    Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2390-2396 
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    Notes: Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi-integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two hierarchies of the known symmetries. Contrary to the general belief, the time-independent symmetry groups of the KdV and mKdV equations are non-Abelian and the infinite dimensional Lie algebras of the KdV and mKdV equations are nonisomorphic though two equations are related by the Miura transformation. Starting from these sets of symmetries, four hierarchies of the integrodifferential KdV equations, which can be solved by the Schrödinger inverse scattering transformation method, are obtained. Some of these hierarchies enjoy a common strong symmetry and/or same local conserved densities.
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    On the equivalence of two super Korteweg–deVries theories: A bi-Hamiltonian viewpoint (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2397-2407 
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    Notes: From a bi-Hamiltonian viewpoint the equivalence of two supersymmetric Korteweg–deVries theories, introduced by Manin–Radul and Laberge–Mathieu, is discussed herein. It is shown that the transformation connecting the two theories (proposed recently in the literature) preserves the bi-Hamiltonian structures; moreover, another derivation of this transformation, stemming from bi-Hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence is presented.
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    Comment on the solutions of the graded Yang–Baxter equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2485-2489 
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    Notes: In this comment we obtain two types of solutions of the graded Yang–Baxter equation whose symmetry group is GLqs(1||1).
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    Reducible Boson fermion realizations for osp(1||2) and osp(3||2) superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2505-2515 
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    Notes: The osp(1||2) algebra is first realized through one boson and two fermion pairs of creation annihilation operators and then both osp(1||2) and osp(3||2) are realized in terms of three boson and two fermion pairs. All these realizations are reducible, and the reduced states are labeled by the total occupation number.
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    Quantized braided groups (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2560-2569 
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    Notes: Algebras that represent a generalization of both quantum groups, quantum supergroups, and braided groups are defined. They are given by a pair of solutions of the Yang–Baxter equation that satisfy some additional conditions. Several examples are presented.
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    On the addition of quantum matrices (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2617-2632 
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    Notes: An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Δ(underbar)t=t⊗1+1⊗t. It supplements the usual comultiplication Δt=t⊗t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m×n quantum matrices. As an application, left-invariant vector fields are constructed on A(R) and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave functions in the lattice approximation of Kac–Moody algebras and other lattice fields can be added and functionally differentiated.
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    Braid group related algebras, their representations and generalized hydrogenlike spectra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3074-3088 
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    Notes: Representations of the n-braid group where generators are given by matrices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Burau representation. Two algebras which are closely related and are physically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator system given by one of the algebras generates a hydrogenlike spectrum.
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    Dissipation in Wigner–Poisson systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1513-1521 
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    Notes: The Wigner–Poisson (WP) system (or quantum Vlasov–Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrödinger–Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi–Markowich and Illner et al.; in particular the Hille–Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
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    Quantum measurements and quantum logics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1555-1572 
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    Notes: A quantum logic formulation of quantum measurements is introduced using Boolean powers of orthomodular σ-posets to the description of the coupled system. A comparison with the traditional Hilbert space approach to quantum measurements and a discussion of some important classes of measurements is given.
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    Nonlinear random wave equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1634-1643 
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    Notes: Nonlinear wave equations describing forced vibrations of a string subject to random perturbations of intensity ε are studied herein. Two kinds of random perturbations are considered; one is Gaussian in the form of initial white noise and the other is a non-Gaussian random forcing which involves the formal derivative of a Brownian sheet. The solutions uε(t,x) of the complete forced equation are a stochastic process in space and time which has a unique stochastic equilibrium. The time variable t varies in a finite interval I:=[0, T], where T is a fixed positive time, and the space variable x varies in an interval J. Assuming that the initial conditions are of sufficient regularity, the fluctuations uε(t,x) from u0(t,x), the unperturbed solution, are analyzed as the intensity of perturbation ε↓0.
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    Motion of particles in five-dimensional Kaluza–Klein space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2423-2429 
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    Notes: Study of radial and circular geodesics including those of tachyons in two spherically symmetric vacuum five-dimensional space–time is done. One of them is of Schwarzschild type and the other the so-called soliton solution. We obtain results which are different from the usual analogous four-dimensional (4D) ones. It is found that all the circular geodesics irrespective of whether they are timelike, null, or spacelike will be stable in the region r(approximately-greater-than)6M. It has also been shown that in a homogeneous cosmological model where the isotropic 3 space expands but the extra space contracts with time, the existence of tachyon is possible. This is in contradiction to the analogous 4D result obtained previously.
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    Bäcklund transformations and zero-curvature representations of systems of partial differential equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2463-2484 
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    Notes: It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.
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    On Schrödinger superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2516-2538 
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    Notes: Using the supersymplectic framework of Berezin, Kostant, and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra) were constructed. An ‘I-type' extension exists in any space dimension, and for any pair of integers N+ and N−. It yields an N=N++N− superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-1/2 particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, ‘exotic' or ‘IJ-type' extensions arise for each pair of integers ν+ and ν−, yielding an N=2(ν++ν−) superalgebra of the type discovered recently by Leblanc et al. in nonrelativistic Chern–Simons theory. For the magnetic monopole the symmetry reduces to o(3)×osp(1/1), and for the magnetic vortex it reduces to o(2)×osp(1/2).
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    Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. I. Typical representations at generic q (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2583-2606 
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    Notes: In the present paper all typical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are constructed at generic deformation parameter q. As in the nondeformed case, the finite-dimensional Uq[gl(2/2)]-module Wq obtained is irreducible and can be decomposed into finite-dimensional irreducible Uq[gl(2)⊕gl(2)]-submodules Vqk.
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    The relation between the Berry and the Anandan–Aharonov connections for U(N) bundles (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1463-1470 
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    Notes: The geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections. In this article we establish the relation between the Berry–Simon and the Anandan–Aharonov definitions for a large class of cyclic Hamiltonians (with N-fold degeneracy) using the classifying theorem for principal fiber bundles.
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    The relativistic Hermite polynomial is a Gegenbauer polynomial (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1549-1554 
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    Notes: It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function. Some examples are given, in particular, related to the asymptotic behavior and to the distribution of zeros of the polynomials for large quantum numbers.
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    Semiclassical approximation for bound states of the Schrödinger equation with a Coulomb-like potential (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1597-1621 
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    Notes: The eigenvalue problem for the radial Schrödinger equation with an "almost'' Coulomb potential is considered. This problem provides the simplest example of a system whose classical trajectories have singularities. Thus the standard semiclassical quantization procedure (in the sense of Einstein–Brillouin–Keller–Maslov) cannot be applied straightforwardly to this situation. The equation under consideration has two transition points on the half axis 0〈x〈∞: a regular singular point at the origin and a turning point for some x0(approximately-greater-than)0; these points coalesce at low energy levels. The well-known comparison equation method provides uniform asymptotics for equations of this kind, but has the following shortcomings: it does not appeal to the corresponding classical mechanical problem and the formulas for the eigenvalues and eigenfunctions contain phase integrals which are not analytic with respect to the parameter characterizing the closeness of the transition points. In the present article we derive new formulas for the eigenfunctions in the form of inverse Fourier transforms of rapidly oscillating exponentials multiplied by some powers of x, together with simple formulas for the eigenvalues. These formulas are directly connected with the classical trajectories and do not have the shortcomings of the comparison equation method, i.e., all the functions entering the asymptotic expansions are analytic in x and energy. As a by-product, an asymptotic expansion of integrals having two stationary phase points which coalesce for some value of the parameter and tend to infinity when the parameter tends to zero is obtained.
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    Energy-momentum conservation in gauge theories (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1668-1687 
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    Notes: Using the formulation in terms of principal fiber bundles, it is shown that the external symmetry implies the conservation of the energy-momentum tensor for a general gauge theory. When applying this theory to the case of Dirac fields, one is naturally forced to replace the dependence on the metric by the dependence on the underlying spin structure in the variational problems.
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    URL: http://dx.doi.org/10.1063/1.530563
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    Superconformal covariantization of superdifferential operator on (1||1) superspace and classical N=2 W superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2570-2582 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study of the superconformal covariantization of superdifferential operators defined on (1||1) superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a Hamiltonian flow defined by the corresponding supersymmetric second Gelfand–Dickey bracket. The covariant form of a superdifferential operator of odd order is given.
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    URL: http://dx.doi.org/10.1063/1.530524
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    The half-Hartley and the half-Hilbert transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2648-2656 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Inversion formulas are obtained for the restrictions of the Hartley and Hilbert transforms to R+. Regularity results are derived, and an illustrative example presented.
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    URL: http://dx.doi.org/10.1063/1.530529
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    Noncommutative geometry for arbitrary braidings (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2633-2647 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The noncommutative geometry corresponding to arbitrary braidings is studied in a purely algebraical way. The new and original proposal of the geometry is given in terms of the theory of braided monoidal categories. The quantum oscillator is considered as an example of application of our geometry.
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    URL: http://dx.doi.org/10.1063/1.530528
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    The m-function for Hamiltonians with Wigner–von Neumann potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1445-1462 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Hamiltonians with strong Wigner–von Neumann potentials are known to possess bound states in the continuous spectrum. For smaller couplings these bound states become resonances, which appear as singularities of the m-function. These singularities are intimately connected with the decay of the corresponding subordinate eigenfunction. For Coulomb-type potentials with Schrödinger operators this has recently be shown by Atkinson, the author, and Hinton, Klaus and Shaw. Here these results are extended to a general class of Wigner–von Neumann potentials for Dirac and Schrödinger operators.
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    URL: http://dx.doi.org/10.1063/1.530600
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    N-body quantum scattering theory in two Hilbert spaces. VII. Real-energy limits (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1487-1512 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study is made of the real-energy limits of approximate solutions of the Chandler–Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator Tπ(z) and an auxiliary operator Mπ(z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator Mπ(z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of Mπ(z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of Tπ(z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories.
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    URL: http://dx.doi.org/10.1063/1.530603
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    Models of q-algebra representations: q-integral transforms and "addition theorems'' (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1951-1975 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case.
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    URL: http://dx.doi.org/10.1063/1.530581
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    On symmetries, conservation laws, and variational problems for partial differential equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1998-2012 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of the correspondence between symmetries and conservation laws for partial differential equations is considered. For Lagrangian systems the set of Noether (variational) symmetries can be shown to lead to the set of all local conservation laws. For partial differential equations without well-defined Lagrangian functions there is no universal correspondence between symmetries and conservation laws. In this article it is shown that for a large class of differential equations there is a natural way to associate conservation laws with symmetries. The class consists of many interesting equations, e.g., Korteweg–de Vries equation, Kadomtsev–Petviashvili equation, Boussinesq equation, nonlinear diffusion equation, Monge–Ampère equation, regularized long-wave equation, and Navier–Stokes equations. Characteristics of the corresponding conservation laws are calculated and examples are given. For Lagrangian systems the consistency of the approach with the standard Noether results is discussed.
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    URL: http://dx.doi.org/10.1063/1.530533
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    A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1066-1094 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A rigorous derivation of the semiclassical Liouville equation for electrons which move in a crystal lattice (without the influence of an external field) is presented herein. The approach is based on carrying out the semiclassical limit in the band-structure Wigner equation. The semiclassical macroscopic densities are also obtained as limits of the corresponding quantum quantities.
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    URL: http://dx.doi.org/10.1063/1.530629
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    Coherent state approach to electron nuclear dynamics with an antisymmetrized geminal power state (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1139-1170 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.
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    URL: http://dx.doi.org/10.1063/1.530632
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    A geometric criterion for adiabatic chaos (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1202-1218 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
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    Five-dimensional axisymmetric stationary solutions as harmonic maps (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1302-1321 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The complete scheme of the application of one- and two-dimensional subspaces and the subgroups method to five-dimensional gravity with a G3 group of motion are presented here in space–time and in potential space formalisms. From this method one obtains the Kramer, Belinsky–Ruffini, Dobiasch–Maison, Clément, Gross–Perry–Sorkin solutions, etc., as special cases.
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    An inequality for Legendre polynomials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1348-1360 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The following inequality is established: ||Pn(cos cursive-theta)||〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, 0〈cursive-theta〈π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos cursive-theta) + (4/π2)× Q2n(cos cursive-theta) 〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of second kind, cos θn1 the largest zero of Qn(x), and cos θn,n+1=−cos θn1. Similarly we obtain the inequalities ||J0(x)|| 〈 [(square root of)1+(π4/16)x4]−1, x≠0, and J20(x) + Y20(x)〈 [(square root of)1+(π4/16)x4]−1, x≥y1, where y1=0.893577... is the first positive zero of Y0(x), and J0(x), Y0(x) denote the Bessel functions of the first and second kind, respectively. The results of the present paper arise out of some problems of nuclear and particle physics.
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    New family of asymptotic solutions of Helmholtz equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1387-1398 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new family of asymptotic solutions of the Helmholtz equation can be derived. It is shown that new solutions are regular at caustics and turning points and do not require any special functions.
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    URL: http://dx.doi.org/10.1063/1.530596
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    Taylor series expansions for eigenvalues and eigenfunctions of parametrized composition operators (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2024-2035 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Operators of the form Tβf(x)=∑Jj=1 cursive-phij(βx)f(σj +ρjx) are considered herein where β is a real parameter; σj and ρj are real numbers, and {cursive-phij} are holomorphic functions which satisfy certain additional conditions. Transfer operators of this form appear in statistical physics: the leading eigenvalue may be interpreted as the free energy of a lattice of interacting particles, as a function of inverse temperature β. A method for obtaining Taylor series expansions in β of the leading and second leading eigenvalues, and the leading eigenfunction are given. The method may be extended to find series expansions for other eigenvalues and eigenfunctions. The radii of convergence of these series have not been found. These results generalize the author's findings in another article [J. Math. Phys. 32, 2718 (1991)].
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    Algebraic structure of parabose Fock space. I. The Green's ansatz revisited (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1054-1065 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green's ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green's ansatz of two (three) terms. Analogs of the form in which the parabose Green's ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.
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    Path integral for the damped harmonic oscillator coupled to its dual (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1185-1191 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
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    URL: http://dx.doi.org/10.1063/1.530634
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    An integrable three-particle system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1219-1232 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.
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    URL: http://dx.doi.org/10.1063/1.530585
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    Resolution of simple singularities yielding particle symmetries in a space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 646-655 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of these cycles is the Dynkin graph of an ADE Lie group, i.e., a Lie group from the cartan series A, D, or E. The deformation of the simple singularity corresponds to ADE symmetry breaking. A (3+1)-dimensional topological model of observation is constructed, transforming consistently under SL(2,C), as an evolving three-dimensional system of world tubes, which connect "possible points of observation.'' The existence of an initial singularity for the four-dimensional space–time is related to its global topological structure. Associating the geometry of ADE singularities to the vertex structure of the topological model puts forward the conjecture on a likewise relation of inner symmetries of elementary particles to local space–time structure.
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