ALBERT

Notes: Canonical Monte Carlo results are presented for mixtures of primitive model electrolytes with a common ion. Both symmetric mixtures, where the ions differ only in size, and charge asymmetric mixtures were studied for ionic strengths ranging from 0.003 to 1.0 M. The hypernetted chain (HNC) equation theory and the simple "exponential'' (EXP) approximation are both applied to the same electrolyte models. The electrolyte mixing coefficients w0 and w1 were calculated from osmotic coefficients. Comparison with Monte Carlo data indicates that the HNC equation yields accurate predictions for the zeroth mixing coefficient w0, while the simple EXP approximation yields qualitatively correct results. The Monte Carlo results for the first mixing coefficient, w1, are not precise enough to allow a quantitative comparison with other theories. However, a strong concentration dependence of w1 for dilute solutions, found previously for the nonprimitive models in the HNC approximation, is confirmed by the Monte Carlo results.

Notes: A new model electron–ammonia pseudopotential parameterized to ab initio quantum chemistry calculations on small lithium ammonia clusters, Li(NH3)n(n=1,4), is studied in a variety of environments. For Li(NH3)n clusters, n=16,32,64,128 the valence electron of the lithium is found to exist in a surface state far from the cation which is localized near the center of mass of the cluster. No bulk states were stabilized. Cluster anions (NH3)−n were also studied and the electron centroid-cluster center of mass probability distribution for (NH3)−64 calculated using umbrella sampling. In the present model, there is apparently no barrier to the dissociation of the surface states. No bulk states were found. This set of results appears to disagree with experiments which have been interpreted to indicate bulk states for cluster anions and the clusters containing lithium. Bulk properties of both a single excess electron and the lithium atom in solution are also reported. The solvation energy agrees well with experiment but the spectrum of the excess electron remains somewhat blue shifted as in earlier calculations. However, the valence electron of the lithium atom is found to spontaneously dissociate; a property not reproduced in previous work.

Notes: The geometrical structures of M+(Ar)n ions, with n=1–14, have been studied by the minimization of a many-body potential surface with a simulated annealing procedure. The minimization method is justified for finite systems through the use of an information theory approach. It is carried out for eight potential-energy surfaces constructed with two- and three-body terms parametrized from experimental data and ab initio results. The potentials should be representative of clusters of argon atoms with first-row transition-metal monocations of varying size. The calculated geometries for M+=Co+ and V+ possess radial shells with small (ca. 4–8) first-shell coordination number. The inclusion of an ion-induced-dipole–ion-induced-dipole interaction between argon atoms raises the energy and generally lowers the symmetry of the cluster by promoting incomplete shell closure. Rotational constants as well as electric dipole and quadrupole moments are quoted for the Co+(Ar)n and V+(Ar)n predicted structures.

Notes: Dynamic light scattering (depolarized Rayleigh and polarized Rayleigh–Brillouin) and quasielastic neutron scattering are employed to study the dynamics of the glass-forming liquid di-2-ethylhexyl phthalate (DOP) (Tg=184 K). The depolarized Rayleigh scattering measurements were made in the temperature range from 303 to 433 K, the polarized Rayleigh–Brillouin measurements in the range from 263 to 433 K, and the quasielastic neutron-scattering measurements in the range from 37 to 312 K and in the Q range from 0.33 to 1.84 A(ring)−1. The orientation times for DOP, obtained from a single Lorentzian fit to the experimental depolarized spectra at high T, are in good agreement with recent dielectric data for the primary (α) relaxation. However, at lower T, the viscosity increases more strongly than the orientation times and the Stokes–Einstein–Debye equation which can adequately describe the dynamics in the high-T range is insufficient at temperatures close to Tg. The relaxation time obtained from the Rayleigh–Brillouin experiment is about 1 order of magnitude faster than the orientation times. In the neutron-scattering experiment we find a strong decrease of the elastic intensity and a corresponding increase of the quasielastic intensity around Tg.The data analysis with respect to the dynamics (from a two Lorentzian fit) revealed the existence of three processes affecting the high-frequency range: (i) a "fast'' (τ2∼10 ps) Q-independent motion with weak T dependence (E2=1.54 kcal/mol), (ii) a "slow'' Q-dependent motion, and (iii) a flat background increasing with T and Q. The fast process is discussed in terms of a very localized motion of the phenyl group (β relaxation) and, as such, as a precursor of the the primary (α) relaxation. The relaxation time of this process (τ2) was found to compare nicely with the time τmax from the Rayleigh–Brillouin (RB) experiment suggesting that the latter is caused by fast localized motions. The slow process is discussed in terms of the jump-diffusion model. The activation energy associated with the jump-diffusion times is 6.1 kcal/mol and it is associated with large-scale diffusional motion of the DOP molecule. The relaxation times obtained from this process are compared with the relaxation times obtained from the depolarized and dielectric techniques for the primary relaxation. Finally, the background can be identified with fast local motions and/or low-frequency excitations relaxing outside the energy window of our experiment.

Notes: We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of "bimolecular'' combination processes L+L' →(L+L') and "unimolecular'' fragmentations L→L'+(L−L'). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalesence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (L¯) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate γ(overdot) and rotational diffusion coefficient Dr. For sufficiently dilute solutions, we find only a weak dependence of L¯ on P. In the semidilute regime, however, an apparent divergence in L¯ at P(approximately-equal-to)1 suggests a flow-induced first-order gelation phenomenon.

Notes: The methods developed in our earlier papers, dealing with Raman scattering from small isolated, spherical particles, uniformly coated with radially uniaxial molecules, are extended to include scattering driven by applied multipolar fields. Such fields are generated by the action of the incident electromagnetic radiation on extraneous material, such as other particles belonging to the same high-density dispersion. In this paper we treat inelastic scattering associated with the Raman dipole matrix elements of the adsorbed molecules ignoring other contributions. Analytical expressions are developed for calculating the primary Raman–Stokes moments given the amplitudes of the applied multipolar fields. As a test of the practicability of the procedure, a full calculation for parallel polarization has been performed for two identical contacting, CO-coated Ag particles oriented with their line of centers parallel to the direction of polarization of the incident radiation. For this case, the effect of interparticle coupling is to broaden and intensify the excitation spectrum, extending the region of intense Raman scattering to much lower frequencies. Intensity enhancements approaching 106 are calculated for frequencies as low as 80% of the single-particle surface-plasmon resonance frequency.

Notes: We have simulated the photodissociation of CH3Br adsorbed at a variety of surfaces. We have considered photodissociation at a smooth LiF (001) substrate and at three rough LiF surfaces which were constructed by removing atoms from the smooth surface. We have also considered photodissociation from several surfaces which have the same structure as the β phase of solid CH3Br to simulate dissociation from high coverages of the adsorbate where CH3Br ice is formed. The simulations were performed using the stochastic classical trajectory method. The asymptotic photofragment kinetic energy and angular distributions were determined and compared with the experimental results of Harrison et al. [J. Chem Phys. 89, 1475 (1988)] and Tabares et al. [J. Chem. Phys. 86, 738 (1987)]. When CH3Br is oriented with CH3 toward a surface, the CH3 kinetic energy distributions are shifted to much lower energies due to energy loss from multiple collisions with Br and the surface; the angular distributions are also significantly broadened. Much of the energy loss in these collisions goes into the translational mode of the Br fragments, causing the Br kinetic energy distributions to have a high-energy tail. When the molecule is in this orientation in a restricted geometry, collisions from the CH3 fragment lead to more effective energy transfer causing the peak of the Br kinetic energy distributions to be shifted to much higher energies and the corresponding angular distributions to become narrower. The main features of the experimental results from photodissociation of CH3Br adsorbed on LiF can be qualitatively explained using the results of the classical trajectory simulations.

Notes: The microscopic properties of the inner surface of the cavities of Anopore and Nuclepore membranes are investigated with scanning electron microscopy (SEM), nitrogen adsorption isotherms, and deuterium nuclear magnetic resonance (2H-NMR). Useful information about the cavity orientation and morphology, and internal surface area is obtained. Analysis of SEM photographs yields estimates of the surface area and the porosity of these membranes which complements the adsorption results. The orientation of liquid crystals permeated in the cavities of Anopore and Nuclepore membranes is probed with the 2H-NMR technique. It is found that the orientation of the liquid crystal molecules is governed by the confining volume and surface conditions. The 2H-NMR spectral line shape of the confined liquid crystal also provides information on the substrate morphology and roughness that is consistent with SEM and adsorption experiments.

Notes: We develop a simple but general three-variable model skeleton to describe complex nonlinear behaviors in electrochemical processes taking place at either a hanging mercury drop electrode (HMDE) or a rotating-disk electrode (RDE). We apply our formalism to the reduction of indium(III) at a HMDE in the presence of thiocyanate, a reaction known to exhibit complex mixed-mode and chaotic oscillations. Besides the role of the negative Faradaic impedance in destabilizing the electrochemical system, mass transport appears to be crucial as the model explicitly takes into account, in a truncated fashion, the time-dependent relaxation of the concentration profile. We study in detail the nonlinear dynamic behavior of our model of the indium/thiocyanate system and a RDE model. The models support mixed-mode sequences that appear either as incomplete Farey sequences or as periodic-chaotic sequences, which we discuss in terms of an incomplete homoclinic scenario whose definition and properties are worked out here. Our results compare very well to the experimental observations in the indium/thiocyanate system and the electrodissolution of a rotating copper disk in phosphoric acid. This satisfactory agreement strongly suggests that diffusion relaxation is an important phenomenon in electrochemical oscillations and could be the essential third variable in many dynamical electrochemical processes.

Notes: The electronic structure of BaH is investigated using a 10-electron relativistic pseudopotential on Ba, frozen core configuration interaction (CI) with three active electrons and core-polarization potential. Fine structure is taken into account with a semiempirical spin–orbit operator. The electronic properties of all states dissociating into Ba(6s2,6s15d1,6s16p1) +H(1s) are obtained and generally found in agreement with experiment within 0.03 A(ring) for equilibrium distances, 300 cm−1 for transition energies, 30 cm−1 for vibrational frequencies, except for the D 2Σ+ state. The methodology used in this work is discussed in the light of the results presented here.

Notes: We study the phase diagram and scattering functions of a ternary mixture of A and B homopolymers, in equal concentrations, and AB diblock copolymer. We locate the disorder line, which marks the appearance of damped oscillatory decaying correlation functions in the system, and also the Lifshitz and equimaxima lines of the structure functions. At these lines, the oscillatory component becomes dominant in a given correlation so that the peak in scattering intensity is no longer at the zero wave vector. We find that while the Lifshitz line of the structure function of all A monomers is quite close to the disorder line, that of A monomers in the homopolymer only is far from it. This shows that the copolymer orders the homopolymers inefficiently, a behavior which is also reflected in the copolymer's weak ability to solubilize them, and which contrasts with the amphiphilic solubilizers of oil and water. The disorder line and all Lifshitz lines meet at a Lifshitz tricritical point. As these ternary mixtures provide a rare opportunity to study this unusual point, we discuss its effects on the structure functions and surface tensions.

Notes: The introduction of a quadratic composition dependent χ into Flory–Huggins theory of binary blends is shown to create three new types of phase behavior in which two pairs of coexisting phases may be present in the two-phase region. This leads, for instance, to an unstable A-rich mixture separating into two A-rich phases instead of A- and B-rich phases.

Notes: The anharmonic potential energy surface of water has been computed ab initio using an augmented coupled cluster method and various basis sets. Whereas the Pople 6–311 G family is manifestly unsatisfactory, Huzinaga–Dunning basis sets perform quite well. The [5s4p2d1f,3s2p] surface reproduces harmonic frequencies and anharmonicity constants to better than about 2 and 1 cm−1, respectively. For quantitative agreement with experiment, both f functions on oxygen and inclusion of core correlation seem to be prerequisite. Comparison with various experimentally derived force fields reveals that the ab initio force field is of comparable quality. From the best computed force field, a set of spectroscopic constants has been derived for all important isotopomers of water. Using a hybrid analytic/direct summation method recently developed by the present authors, the thermodynamic functions gef(T), hcf(T), S0, and Cp are computed including exact account of anharmonicity and rovibrational coupling, and very good analytical approximations to centrifugal distortion and quantum rotation effects. The computed functions substantially revise previous literature results at high temperatures. Differences between thermodynamic functions from various computed force fields are an order of magnitude smaller than these errors. Thermodynamic tables in JANAF style from 100 to 3000 K, as well as a full set of rovibrational spectroscopic constants, are presented. It is concluded that obtaining force fields of near-spectroscopic accuracy, and thermodynamic tables of very high accuracy, is presently feasible for small polyatomic molecules.

Notes: The collective dynamics of liquid methanol-d4 is studied by means of molecular-dynamics simulation. The model potential is validated by means of lattice energy calculations and shows a very good agreement with the experimentally obtained crystal structure. Center-of-mass density and momentum fluctuations are investigated in the (Q,ω) region which is also accessible to inelastic neutron-scattering (INS) techniques. A simple viscoelastic model previously used for the analysis of INS data is tested against the dynamic structure factor computed from the simulation. A direct comparison with the INS results themselves is also made and qualitative agreement is found. Also, a tentative assignment of the peaks appearing in the current–current correlations is made on the basis of lattice-dynamics calculations for the polycrystalline low-temperature α phase.

Notes: A small-angle light-scattering experiment probing the time-dependent behavior of a semidilute polymer solution under simple shear is presented. Specifically, this paper investigates time-dependent anisotropic growth and orientation of concentration fluctuations in a semidilute solution of polystyrene in dioctyl phthalate above the quiescent cloud-point temperature. Two flow cells, which permitted investigation of the structure and dynamics of concentration fluctuations in both the flow-shear and the flow-vorticity planes, were used. Concentration fluctuations were found to be enhanced anisotropically by the shear flow in both planes. In the flow-vorticity plane, shear-enhanced concentration fluctuations orient along the vorticity direction, while in the flow-shear plane, the axis of average orientation is at an angle between 135° and 45° to the direction of flow. Qualitative trends of this anisotropic growth of concentration fluctuations are in agreement with the predictions of the Helfand–Fredrickson model in the flow-shear plane. Furthermore, the Onuki–Doi theory relating the scattering dichroism to the structure factor has been verified experimentally by comparing scattering dichroism calculated from scattering patterns with previous experimentally measured dichroism. Scattering dichroism, both calculated from structure factors and experimentally determined over a range of shear rates and temperatures, is demonstrated to depend only on the Weissenberg number. Relaxation of shear-enhanced fluctuations on cessation of flow allowed for the calculation of a diffusion coefficient.

Notes: A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is "partially solvable" if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on D=1, D=2, and D≥2, and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models. © 1999 American Institute of Physics.

Notes: A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed. © 1999 American Institute of Physics.

Notes: We consider the Manev potential, given by the sum between the inverse and the inverse square of the distance, in an anisotropic space, i.e., such that the force acts differently in each direction. Using McGehee coordinates, we blow up the collision singularity, paste a collision manifold to the phase space, study the flow on and near the collision manifold, and find a positive-measure set of collision orbits. Besides frontal homothetic, frontal nonhomothetic, and spiraling collisions and ejections, we put into the evidence the surprising class of oscillatory collision and ejection orbits. Using the infinity manifold, we further tackle capture and escape solutions in the zero-energy case. By finding the connection orbits between equilibria and/or cycles at impact and at infinity, we describe a large class of capture-collision and ejection-escape solutions. © 1999 American Institute of Physics.

Notes: We discuss a finite rectangular well of a depth λ2 as a perturbation for the infinite one with λ as a perturbation parameter. In particular, we consider a behavior of energy levels in the well as functions of complex λ. It is found that all the levels of the same parity are defined on infinitely sheeted Riemann surfaces whose topological structures are described in detail. These structures differ considerably from those found in models investigated earlier. It is shown that perturbation series for all the levels converge what is in a contrast with the known results of Bender and Wu. The last property is shown to hold also for the infinite rectangular well with the Dirac delta barrier as a perturbation considered earlier by Ushveridze. © 1999 American Institute of Physics.

Notes: The Calabi–Yau and Joyce manifolds used in string and M-theory compactifications have no continuous groups of isometries, but they often have nontrivial discrete (actually finite) isometry groups. Discrete isometries of nonsimply connected Riemannian manifolds do not necessarily map spin structures into themselves, however; thus, inconsistencies are possible if a spin connection is used to construct the gauge vacuum. We consider this problem in detail and show how it may be avoided. © 1999 American Institute of Physics.

Notes: We introduce and perform a systematic study of a new exactly solvable model of sphere interactions in quantum mechanics : the δ′ interaction, formally given by −Δ+αδ′(|x|−R), x∈R3, R〉0, α∈R. We also consider the cases of a δ′ plus a Coulomb interaction and finitely many δ′-sphere interactions with support on concentric spheres. For all these models, we provide basic properties and discuss the stationary scattering theory. We also briefly discuss the δ′-sphere interaction of the second type. © 1999 American Institute of Physics.

Notes: It is widely believed that Bell has proved there can be no consistent local extension of the quantum formalism. Against this, Angelidis has presented a hidden variable theory which, he claims, makes precisely the same predictions as the quantum formalism and which also satisfies locality. In this note, we argue that Angelidis' theory does not live up to its inventor's claims. © 1999 American Institute of Physics.

Notes: The quantum mechanics of a spin 〈fraction SHAPE="CASE"〉12 particle on a locally spatial constant curvature part of a (2+1)-space–time in the presence of a constant magnetic field of a magnetic monopole has been investigated. It has been shown that these two-dimensional Hamiltonians have the degeneracy group of SL(2,c), and para-supersymmetry of arbitrary order or shape invariance. Using this symmetry we have obtained its spectrum algebraically. The Dirac's quantization condition has been obtained from the representation theory. Also, it is shown that the presence of angular deficit suppresses both the degeneracy and shape invariance. © 1999 American Institute of Physics.

Notes: A boundary value problem for a 2×2 S-matrix is solved by the method of projection matrices. The S-matrix is assumed to be diagnoalized by orthogonal matrix U(k2)=Ω(k2)/det Ω(k2), where matrix elements of Ω(k2) are polynomials. The equation det Ω(k2)=0 has roots of any order. The example is considered for the roots with order 2. © 1999 American Institute of Physics.

Notes: We discuss the classical mechanics on the Grassmannian and the disc modeled on the ideal L(2,∞). We apply methods of geometric quantization to these systems. Their relation to a flat symplectic space is also discussed. © 1999 American Institute of Physics.

Notes: The w∞ algebra is a higher-spin extension of the Virasoro algebra. In this paper, we construct the gauge theory of w symmetry in terms of its representations. © 1999 American Institute of Physics.

Notes: Inönü–Wigner contractions from the rotation group O(n+1) to the Euclidean group E(n) are used to relate the separation of variables in Laplace–Beltrami operators on n-dimensional spheres and Euclidean spaces, respectively. In this article we consider all subgroup type coordinates corresponding to different chains of subgroups of O(n+1) and E(n), respectively. In particular, the contractions relate the graphical formalism of "trees" on spheres to the "clusters" on Euclidean spaces (introduced in this article). The contractions are considered analytically on several levels: the vector fields realizing the Lie algebras, the complete sets of commuting operators characterizing separable coordinate systems, the coordinate systems themselves and the separated eigenfunctions. © 1999 American Institute of Physics.

Notes: We present and study a class of functions associated with the two-particle quantum relativistic Calogero–Moser system with elliptic interactions. The functions may be viewed as joint eigenfunctions of two independent commuting analytic difference operators, one of which is the defining quantum dynamics; The second one is obtained by interchanging the step size and the imaginary period. The functions depend on parameters that are dense in the natural parameter domain. In essence, they consist of products of Weierstrass σ-functions and plane waves. The zeros of the σ-functions satisfy a constraint system encoding both Schrödinger equations at once. © 1999 American Institute of Physics.

Notes: For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows corresponding to the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two-dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature, the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. For each domain there is also a one-parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh effect. © 1999 American Institute of Physics.

Notes: An iterative map of the unit disk in the complex plane is used to explore certain aspects of self-dual, four-dimensional gauge fields (quasi)periodic in the Euclidean time. These fields are characterized by two topological numbers and contain standard instantons and monopoles as different limits. The iterations do not correspond directly to a discretized time evolution of the gauge fields. They are implemented in an indirect fashion. First, (t,r,θ,φ) being the standard coordinates, the (r,t) half-plane is mapped on the unit disk in an appropriate way. This provides an (r,t) parametrization of Z0, the starting point of the iterations and makes the iterates increasingly complex functions of r and t. These are then incorporated as building blocks in the generating function of the fields. We explain in what sense and to what extent some remarkable features of our map (indicated in the title) are thus carried over into the continuous time development of the fields. Special features for quasiperiodicity are studied. Spinor solutions and propagators are discussed from the point of view of the mapping. Several possible generalizations are indicated. Some broader topics are also discussed. © 1999 American Institute of Physics.

Notes: We derive a generalized Gel'fand–Levitan integral equation for two block Ablowitz–Kaup–Newell–Segur systems. This is possible if we suppose that the matrix coupling coefficients are invertible and come from simple zeroes of the determinant of the diagonal blocks of the scattering matrix. © 1999 American Institute of Physics.

Notes: A general discussion is given of weak limits of classical dynamical systems depending on a parameter. The resulting maps are shown to be invertible if and only if they define a group of measure preserving point transformations. The irreversible case automatically leads to positive bistochastic maps and is characterized in terms of convergence properties of the corresponding automorphisms of the observable algebra. Necessary and sufficient conditions are given for the limit to define a time-independent Markov process. Two models are discussed, for a particle in a periodic potential, and for a particle interacting with fixed configurations of external obstacles. © 1999 American Institute of Physics.

Notes: A classification of variationally trivial Lagrangians on T*M which are invariant under the Lie algebra of infinitesimal gauge transformations of the principal bundle π:M×U(1)→M, is given. A characterization of Lagrangian densities on T*M which are invariant under the Lie algebra of all infinitesimal automorphisms of M×U(1) is also obtained. © 1999 American Institute of Physics.

Notes: In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present, i.e., the fluid moves in R2. In this case we know that, when the diameter σ of each region supporting the vorticity is very small, the time evolution of the fluid is quite well described by a dynamical system with finite degrees of freedom called the "point vortex model." In particular the connection between this model and the Euler equation has been proved rigorously as σ→0. In the present paper we discuss the "stability" of the point vortex model with respect to a particular small perturbation of the planar symmetry. More precisely we consider a fluid moving in R3 with a cylindrical symmetry without swirl in which each vortex is no longer a straight tube, but a vorticity ring. We prove that large annuli of radii r(approximate)σ−β for any β〉0 remain "localized" and hence we obtain the point vortex model as σ→0. © 1999 American Institute of Physics.

Notes: Multidimensional gravity interacting with intersecting electric and magnetic p-branes is considered for fields depending on a single variable. Some general features of the system behavior are revealed without solving the field equations. Thus, essential asymptotic properties of isotropic cosmologies are indicated for different signs of spatial curvature; a no-hair-type theorem and a single-time theorem for black holes are proved (the latter makes sense in models with multiple time coordinates). The validity of the general observations is verified for a class of exact solutions known for the cases when certain vectors, built from the input parameters of the model, are either orthogonal in minisuperspace, or form mutually orthogonal subsystems. From the nonexistence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any p-brane system. © 1999 American Institute of Physics.

Notes: Computations of the strong field generation of gravitational waves by black hole processes produces waveforms that are dominated by quasinormal (QN) ringing, a damped oscillation characteristic of the black hole. We describe here the mathematical problem of quantifying the QN content of the waveforms generated. This is done in several steps: (i) We develop the mathematics of QN systems that are complete (in a sense to be defined) and show that there is a quantity, the "excitation coefficient," that appears to have the properties needed to quantify QN content. (ii) We show that incomplete systems can (at least sometimes) be converted to physically equivalent complete systems. Most notably, we give a rigorous proof of completeness for a specific modified model problem. (iii) We evaluate the excitation coefficient for the model problem, and demonstrate that the excitation coefficient is of limited utility. We finish by discussing the general question of quantification of QN excitations, and offer a few speculations about unavoidable differences between normal mode and QNM systems. © 1999 American Institute of Physics.

Notes: The motivation for the present paper lies in the fact that the literature concerning the Coulomb wave functions FL(η,ρ) and GL(η,ρ) is a jungle in which it may be hard to find a safe way when one needs general formulas for the Coulomb wave functions with complex values of the variable ρ and the parameters L and η. For the Coulomb wave functions and certain linear combinations of these functions we discuss the connection with the Whittaker function, the Coulomb phase shift, Wronskians, reflection formulas (L→−L−1), integral representations, series expansions, circuital relations (ρ→ρe±iπ) and asymptotic formulas on a Riemann surface for the variable ρ. The parameters L and η are allowed to assume complex values. © 1999 American Institute of Physics.

Notes: The osp(1,2)-covariant Lagrangian quantization of irreducible gauge theories is generalized to L-stage reducible theories. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case is discussed and Ward identities related to osp(1,2) symmetry are given. Massive first-stage theories with closed gauge algebra are studied in detail. The generalization of the Chapline–Manton model and topological Yang–Mills theory to the case of massive fields are considered as examples. © 1999 American Institute of Physics.

Notes: We establish the Schlieder and the Borchers property for thermal field theories. In addition, we provide some information on the commutation and localization properties of projection operators. © 1999 American Institute of Physics.

Notes: A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in this approach no exact divergencies appear and no renormalization is needed. The starting point of the consideration is the representation of the zeta functions in terms of contour integral, further the uniform asymptotic expansion of the Bessel function is essentially used. After the analytic continuation, needed for calculating the Casimir energy, the zeta functions are presented as infinite series containing the Riemann zeta function with rapidly falling down terms. The spectral zeta functions are constructed exactly for a material ball and infinite cylinder placed in a uniform endless medium under the condition that the velocity of light does not change when crossing the interface. As a special case, perfectly conducting spherical and cylindrical shells are also considered in the same line. In this approach one succeeds, specifically, in justifying, in mathematically rigorous way, the appearance of the contribution to the Casimir energy for cylinder which is proportional to ln(2π). © 1999 American Institute of Physics.

Notes: The Wigner–Weyl quantum-to-classical correspondence rule is nonunique with respect to coordinate choice. This ambiguity can be exploited to improve the accuracy of semiclassical approximations. For instance, the well-known Langer modification was recently derived by applying a coordinate transformation to the radial Schrödinger equation prior to using the Wigner–Weyl rule—albeit only by presuming exact quantum solutions for all nonradial degrees of freedom [J. J. Morehead, J. Math. Phys. 36, 5431 (1995)]. In this paper, the full classical Hamiltonian is derived in all degrees of freedom, using a (hyper)spherical coordinate Wigner–Weyl correspondence with a Langer-like modification of polar angles. For central force Hamiltonians, the new result is radially equivalent to that of Langer, and to the standard Cartesian form. The new correspondence is superior with respect to all angular momentum operators however, in that the resultant semiclassical eigenvalues are exact—a desirable goal, evidently achieved here for the first time. © 1999 American Institute of Physics.

Notes: Harmonic maps from S2 to CPN−1 are introduced to construct low-energy configurations of the SU(N) Skyrme model. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only a little higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon and energy densities of the SU(3) configurations with baryon number B=3−6 are more symmetrical than their SU(2) analogs, thus suggesting that there exist solutions of the model with these symmetries. We also show that any SU(2) solution embedded into the SU(4) Skyrme model becomes a topologically trivial solution of this model. © 1999 American Institute of Physics.

Notes: In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations. © 1999 American Institute of Physics.

Notes: Multidimensional model describing the cosmological evolution and/or spherically symmetric configuration with n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M0 has a nonzero curvature, and all p-branes do not "live" in M0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically symmetric solutions (containing nonextremal p-brane black holes) is considered. Post-Newtonian parameters are calculated. © 1999 American Institute of Physics.

Notes: We estimate from above the set of knots, Ω(n,μ), generated by closure of the n-string 1+1- and 2+1-dimensional braids of irreducible length μ(μ(very-much-greater-than)1) in the limit n(very-much-greater-than)1. © 1999 American Institute of Physics.

Notes: Binary constrained flows of soliton equations admitting 2×2 Lax matrices have 2N degrees of freedom, which is twice as many degrees of freedom than in the case of monoconstrained flows. By using the normal method, their Lax matrices directly give rise to first N pairs of canonical separated variables for their separation of variables. We propose a new method to introduce the other N pairs of canonical separated variables and additional separated equations. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies. © 1999 American Institute of Physics.

Notes: An algorithm is presented for the evaluation of the even moments of the end-to-end separation of a polymer chain. The only assumption made in the distribution function is that the energy of the chain depends only on the individual bond lengths of the chain. This assumption covers many of the commonly used distribution functions. © 1999 American Institute of Physics.

Notes: We give a simple proof of the Ališauskas–Jucys triple sum formula for Wigner 9j-symbols. © 1999 American Institute of Physics.

Notes: The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse index theorem for Riemannian geodesics with two variable endpoints, in the spirit of the original Morse proof. This approach reduces substantially the effort required in the proofs of the theorem given previously [Ann. Math. 73(1), 49–86 (1961); J. Diff. Geom 12, 567–581 (1977); Trans. Am. Math. Soc. 308(1), 341–348 (1988)]. Exactly the same argument works also in the case of timelike geodesics between two submanifolds of a Lorentzian manifold. For the extension to the lightlike Lorentzian case, just minor changes are required and one obtains easily a proof of the focal index theorem previously presented [J. Geom. Phys. 6(4), 657–670 (1989)]. © 1999 American Institute of Physics.

Notes: We show that certain two-term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups. For the transformations of nonterminating 3φ2 series, and those of terminating balanced 4φ3 series, these invariance groups are symmetric groups. For transformations of 2φ1 series the invariance group is the dihedral group of order 12. Transformations of terminating 3φ2 series are described by means of some subgroup of S6, and finally the invariance group of transformations of very-well-poised nonterminating 8φ7 series is shown to be isomorphic to the Weyl group of a root system of type D5. © 1999 American Institute of Physics.

Notes: In this paper the concepts of almost Hermitian and Kählerian supermanifolds are introduced. Using the classical Newlander–Nirenberg theorm, it is shown that an almost complex structure J is integrable if it is compatible with ΔL, the supermanifold analog of the Levi-Civita connection. It is proved that an almost Hermitian supermanifold is Kählerian if and only if ΔL is compatible with J. © 1999 American Institute of Physics.

Notes: By using the field–antifield formalism, we show that the method of Batalin, Fradkin, Fradkina, and Tyutin (BFFT) to convert Hamiltonian systems submitted to second class constraints introduces compensating fields which do not belong to the BRST cohomology at ghost number one. This assures that the gauge symmetries which arise from the BFFT procedure are not obstructed at quantum level. An example where massive electrodynamics is coupled to chiral fermions is considered. We solve the quantum master equation for the model and show that the respective counterterm has a decisive role in extracting anomalous expectation values associated with the divergence of the Noether chiral current. © 1999 American Institute of Physics.

Notes: Canonical quantization of a Chern–Simons gauge field minimally coupled to a spinor field is studied as an indefinite metric quantum field theory in the usual covariant gauges, by using a lattice cutoff. For this model, we show that positivity for the indefinite metric, Gauss' Law, gauge invariance and Osterwalder–Schrader positivity for a self-adjoint Hamiltonian are equivalent. In addition, the path-space formula for the Osterwalder–Schrader semigroup is constructed in terms of a Euclidean scalar, massive, Gaussian random field. © 1999 American Institute of Physics.

Notes: Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide explicit examples for spherically symmetric SU(N) monopoles with various symmetry breakings. In particular we show how to obtain these monopoles from harmonic maps into complex projective spaces. The approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spherically symmetric SU(N) hyperbolic monopoles. © 1999 American Institute of Physics.

Notes: We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings. © 1999 American Institute of Physics.

Notes: We show that certain partial differential equations associated to nonisospectral scattering problems in 2+1 dimensions provide a key to associated integrable hierarchies of both ordinary and partial differential equations. This is illustrated using (an extension of) a known second-order and two new third-order nonisospectral scattering problems. These scattering problems allow us to derive new hierarchies of integrable partial differential equations, in both 1+1 and 2+1 dimensions, together with their underlying linear problems (isospectral and nonisospectral); and also new hierarchies of integrable ordinary differential equations, again with their underlying linear problems. © 1999 American Institute of Physics.

Notes: In an open time-convex region Λ of a strongly causal Lorentzian manifold (M,g), we consider an event p and a timelike, injective curve γ. We look for geodesics connecting p and γ in Λ and satisfying the conservation law g(z)[z(overdot),z(overdot)]=−E for a fixed E〉0. It is already known that such geodesics are the stationary points of the arrival time functional τ. Our main result is to prove the existence of a decreasing flow for τ, by means of a shortening procedure. This makes possible to apply to τ global variational methods obtaining existence and multiplicity results (using the Ljusternik–Schnirelmann category theory) and also to develop a Morse theory. © 1999 American Institute of Physics.

Notes: For the description of space–time fermions, Dirac–Kähler fields (inhomogeneous differential forms) provide an interesting alternative to the Dirac spinor fields. In this paper we develop a similar concept within the symplectic geometry of phase spaces. Rather than on space–time, symplectic Dirac–Kähler fields can be defined on the classical phase space of any Hamiltonian system. They are equivalent to an infinite family of metaplectic spinor fields, i.e., spinors of Sp(2N), in the same way an ordinary Dirac–Kähler field is equivalent to a (finite) multiplet of Dirac spinors. The results are interpreted in the framework of the gauge theory formulation of quantum mechanics which was proposed recently. An intriguing analogy is found between the lattice fermion problem (species doubling) and the problem of quantization in general. © 1999 American Institute of Physics.

Notes: We construct a free field realization of vertex operators of the dilute AL models along with the Felder complex. For L=3, we also study an E8 structure in terms of the deformed Virasoro currents. © 1999 American Institute of Physics.

Notes: We present the covariant generalization of the Dirac equation in a nonfactorizable metric and give the corresponding exact solutions in terms of special functions as well as the explicit form of the spinor solution. Then we treat the particular case of the Weyl equation for the neutrinos. © 1999 American Institute of Physics.

Notes: Let (l−k2)u=−u″+q(x)u−k2u=δ(x), x∈R, ∂u/∂|x|−iku→0, |x|→∞. Assume that the potential q(x) is real valued and compactly supported: q(x)=q(x), q(x)=0 for |x|≥1, ∫−11|q|dx〈∞, and that q(x) produces no bound states. Let u(−1,k) and u(1,k), ∀k〉0 be the data. It is shown that under the above assumptions these data determine q(x) uniquely. © 1999 American Institute of Physics.

Notes: A K slicing of the Reissner–Nordstrom (RN) spacetime is shown to provide a complete foliation of the region up to the inner horizon, and the horizon to correspond to the limit as K→±∞. The implications of this foliation in the context of York time are discussed. © 1999 American Institute of Physics.

Notes: This paper extends the investigation of the invariants of the Riemann tensor to include the invariants that are of odd degree in the trace-free Ricci tensor. It is shown that these invariants can be expressed in terms of 15 such invariants that are irreducible. As a consequence, it is possible to write down a complete set of invariants of the Riemann tensor. Several syzygies for these invariants have been found and examples of these are given. These syzygies suggest there may be several new syzygies of invariants with even degree in the trace-free Ricci tensor. A large number of these have also been found and are discussed in the paper. © 1999 American Institute of Physics.

Notes: For the first time, exact solutions for the full self-consistent Einstein–Yang–Mills–Dirac systems with gauge groups SU(2) and SU(4) in Robertson–Walker space–time R×S3 are presented, which are symmetric under the action of the group SO(4) of spatial rotations. The approach is based on the dimensional reduction method for gauge, spinor, and gravitational fields and relates symmetric solutions in EYMD theory to certain solutions of an effective dynamic system. The solutions are interpreted as solutions of the cosmological type with an oscillating Yang–Mills field, which exchanges energy with a spinor field. The explicit form of the solution for the spinor field shows that its energy changes the sign in the process of the evolution of the Yang–Mills field from one vacuum to another. © 1999 American Institute of Physics.

Notes: The explicit denominator (normalization) function of the canonical tensor operators of the quantum algebra uq(3), corresponding to the maximal null space case is derived ab initio in terms of double basic hypergeometric series, which cannot be obtained as any q-extension of the SU(3) denominator polynomial Gb″1(Δ,x) in terms of multiple (double or triple) balanced hypergeometric series, introduced by Biedenharn, Louck, and their collaborators (although their q=1 versions are shown being equivalent). The corresponding orthonormal seed isoscalar factors of the coupling (Wigner–Clebsch–Gordan) coefficients of uq(3) and SU(3) with multiple irreducible representations are presented. Conjectured expression of the q-polynomials [which ratios appear in the uq(3) and (new) SU(3) denominator functions for an arbitrary value of the canonical multiplicity label t of the repeating irreducible representations] in terms of multiple partition dependent q-series (extension of the maximal and minimal null space versions) is presented and considered. © 1999 American Institute of Physics.

Notes: We derive Galilean wavelets, by which we mean coherent states of the affine Galilei group, that is, the Galilei group extended by independent space and time dilations. The construction follows a general method based on square integrable group representations, possibly modulo a subgroup, i.e., on a homogeneous space of the underlying group. We also examine the restriction to the Schrödinger subgroup, which contains only dilations that leave invariant the Schrödinger and the heat equations. © 1999 American Institute of Physics.

Notes: We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-Abelian version of Stokes' theorem. © 1999 American Institute of Physics.

Notes: We describe the construction of some finite dimensional nonunitary representations of E(2), the Lie group of Euclidean transformations in the plane. Some properties of these representations are also discussed, with emphasis on indecomposable representations. © 1999 American Institute of Physics.

Notes: A four-field lattice furnished by Blaszak and Marciniak is transformed into bilinear form upon introducing two auxiliary independent variables. A Bäcklund transformation in bilinear form is found for the lattice and the corresponding nonlinear superposition formula is rigorously established. As a consequence, soliton solutions to the lattice are derived. © 1999 American Institute of Physics.

Notes: From the bicovariant first-order differential calculus on inhomogeneous Hopf algebra B we construct the set of right-invariant Maurer–Cartan one-forms considered as a right-invariant basis of a bicovariant B-bimodule over which we develop the Woronowicz general theory of differential calculus on quantum groups. In this formalism, we introduce suitable functionals on B which control the inhomogeneous commutation rules. In particular, we find that the homogeneous part of commutation rules between the translations and those between the generators of the homogeneous part of B and translations are controlled by different R-matrices satisfying characteristic equations. © 1999 American Institute of Physics.

Notes: © 1999 American Institute of Physics.

Notes: The Landau–Lifshitz equation is derived as a first-order iteration of the Lorentz–Dirac equation for the charged particle. In those cases with null electromagnetic field's gradient, the Landau-Lifshitz gives the so named Herrera equation. A general method for the solution of the latter equation is presented and applied to the motion of a particle in a uniform electromagnetic field. © 1999 American Institute of Physics.

Notes: It is shown that the trajectories of a charged particle in a static magnetic field and a velocity-independent potential in a three-dimensional space are (the projection of) the geodesics of a suitably defined metric in a four-dimensional space. It is shown that each one-parameter group of isometries of the original configuration space that leaves the magnetic field invariant gives rise to a one-parameter group of isometries of the metric defined on the four-dimensional space and, hence, to a constant of the motion. It is also shown, similarly, that the Schrödinger equation for a charged particle in a static magnetic field is equivalent to the Schrödinger equation for a free particle in the four-dimensional space mentioned above. © 1999 American Institute of Physics.

Notes: Euclidean and Minkowski four-space uniqueness theorems are derived which yield a new perspective of classical four-vector fields. The Euclidean four-space uniqueness theorem is based on a Euclidean four-vector identity which is analogous to an identity used in Helmholtz's theorem on the uniqueness of three-vector fields. A Minkowski space identity and uniqueness theorem can be formulated from first principles and the space components of this identity turn out to reduce to the three-vector Helmholtz's identity in a static Newtonian limit. A further result is a uniqueness theorem for scalar fields based on an identity which is proved to be a static Newtonian limit of the zeroth or scalar component of the Minkowski space extension of the Helmholtz identity. Last, the three-vector Helmholtz identity and uniqueness theorem and their four-space extensions to Minkowski space are generalized to mass damped fields. © 1999 American Institute of Physics.

Notes: In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical space–time to be singularity free. The applicability of the theorem is tested on examples provided by the literature that are known to have regular curvature invariants. © 1999 American Institute of Physics.

Notes: We propose the (BRST-invariant) quantum open superstring field theory in the "B0-gauge," based on Neveu–Schwarz (NS) strings in 1 picture and Ramond (R) strings in 〈fraction SHAPE="CASE"〉12 picture. We give the propagators of these open NS and R superstrings. In order to obtain the BRST-invariant interaction terms among these superstrings, we modify the interaction terms among three superstrings (i.e., among NS–NS–NS and R–R–NS) by subtracting the infinite number of counter terms, each of which involves interaction terms among "more than four superstrings." The modified action can be obtained successively, so that resulting amplitudes in g-loops should become BRST invariant. Thus obtained amplitudes are referred to as the "amputated scatts," with the help of which the physical scattering amplitudes can be expressed. These physical scattering amplitudes among NB bosonic (NF fermionic) particles are calculated by using the analytic inlint gluing operator (which has already been proposed and used in the quantum bosonic string field theory "in the B0=0 gauge"). © 1999 American Institute of Physics.

Notes: We derive transport equations from a general class of equations of form iut=H(X,D)u+V(X,D)u where H(X,D) and V(X,D) are pseudodifferential operators (Weyl operator) with symbols H(x,k) and V(x,k), where H(x,k) being polynomial in k and smooth in x,V(x,k) is a mean zero random function and is stationary in space variable. We also consider system of equations in the above form. Such equations cover many of the equations that arise in wave propagations, such as those considered in a paper by Ryzhik, Papanicolaou, and Keller [Wave Motion 24, 327–370 (1996)]. Our results generalize those by Ryzhik, Papanicolau, and Keller. © 1999 American Institute of Physics.

Notes: Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are determined. Widely applied models in Physics are shown to appear as particular cases of the method. © 1999 American Institute of Physics.

Notes: The stochastic functional method is applied to plane-wave scattering from a random cylindrical surface, whereupon the Dirichlet boundary condition is rigorously imposed. Analytical results, accurate to second and fourth order in surface roughness, are obtained for the coefficients of the Wiener–Hermite expansion of the secondary scattered wave field. The validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion. The former, which is introduced herein, states that any approximate solution should be in conformity with the boundary condition, whereas the latter pertains to the energy conservation law. The numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration. Moreover, it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion; the latter may lead to underestimating deficiencies of the approximate solution under test. © 1999 American Institute of Physics.

Notes: The classical n-dimensional Calogero–Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion. In the first part of the article some properties related with the existence of several families of constants of motion are analyzed. In the second part, the master symmetries and the time-dependent symmetries of this system are studied. © 1999 American Institute of Physics.

Notes: An ideal fluid whose internal energy depends on density, density gradient, and entropy is considered. Dynamic equations are integrated, and a description in terms of hydrodynamic (Clebsch) potentials occurs. All essential information on the fluid flow (including initial and boundary conditions) appears to be carried by the dynamic equations for hydrodynamic potentials. Information on initial values of the fluid flow is carried by arbitrary integration functions. Initial and boundary conditions for potentials contain only nonessential information concerning the fluid particle labeling. It is shown that the description in terms of n-component complex wave function is a kind of such description in terms of hydrodynamic potentials. Spin determined by the irreducible number nm of the wave function components appears to be an attribute of the fluid flow. Classification of fluid flows by the spin appears to be connected with invariant subspaces of the relabeling group. © 1999 American Institute of Physics.

Notes: A subclass of a recently discovered class of solutions in multidimensional gravity with intersecting p-branes related to Lie algebras and governed by a set of harmonic functions is considered. This subclass in case of three Euclidean p-branes (one electric and two magnetic) contains a cosmological solution to D=11 supergravity related to hyperbolic Kac–Moody algebra F3 (of rank 3). This solution describes the non-Kasner power-law inflation. © 1999 American Institute of Physics.

Notes: In this work we describe a general class of dispersive N-body Hamiltonians for which we prove the Hunziker, van Winter, and Zislin (HWZ) theorem and a Mourre estimate outside a closed and countable set of energies called thresholds. As a consequence of the Mourre estimate we prove a strong form of the limiting absorption principle, which implies the absence of a singular continuous spectrum and gives criteria of local smoothness. © 1999 American Institute of Physics.

Notes: It is shown that there exists a one-to-one correspondence between the real solutions of the Einstein vacuum field equations linearized about the Minkowski metric and the (complex) metric perturbations whose curvature to first order in the metric perturbation is self-dual. It is also shown that the self-duality condition of the curvature to first order in the metric perturbation is equivalent to a set of first-order equations for the metric perturbation whose solution is given by a scalar potential that obeys the wave equation. © 1999 American Institute of Physics.

Notes: Prepotentials in N=2 supersymmetric Yang–Mills theories are known to obey nonlinear partial differential equations called Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations. In this paper, the prepotentials at the one-instanton level in N=2 supersymmetric SU(4) Yang–Mills theory are studied from the standpoint of WDVV equations. Especially, it is shown that the one-instanton prepotentials are obtained from WDVV equations by assuming the perturbative prepotential and by using the scaling relation as a subsidiary condition but are determined without introducing the Seiberg–Witten curve. In this way, various one-instanton prepotentials which satisfy both WDVV equations and the scaling relation can be derived, but it turns out that among them there exist one-instanton prepotentials which coincide with the instanton calculus. © 1999 American Institute of Physics.

Notes: The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian. © 1999 American Institute of Physics.

Notes: The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds Γ(backward-slash)Hd and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.© 1999 American Institute of Physics.

Notes: It is argued that geometric algebra, in the form of the multiparticle spacetime algebra, is well suited to the study of multiparticle quantum theory, with advantages over conventional techniques both in ease of calculation and in providing an intuitive geometric understanding of the results. This is illustrated by comparing the geometric algebra approach for a system of two spin-1/2 particles with the nonrelativistic approach of Holland [Phys. Rep. 169, 294 (1988)]. © 1999 American Institute of Physics.

Notes: We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schrödinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field E(vector)(t) through the Stark Hamiltonian H=λ(J(vector)⋅E(vector))2. © 1999 American Institute of Physics.

Notes: Under a constraint between the potentials and the eigenfunctions, the 3×3 AKNS matrix spectral problem and its adjoint spectral problem associated with the three-wave interaction equations are nonlinearized so as to be a new finite-dimensional Hamiltonian system. A general scheme for generating involutive systems of conserved integrals and their two new generators are proposed, by which the finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Moreover, the involutive solutions of the three-wave interaction equations are given. © 1999 American Institute of Physics.

Notes: Let (P,π,B,G) be a G-principal fiber bundle. The action of G on the cotangent bundle T*P is free and Hamiltonian. By Liberman and Marle [Symplectic Geometry and Analytical Mechanics (Reidel, Dortrecht, 1987)] and Marsden and Ratiu [Lett. Math. Phys. 11, 161 (1981)] the quotient space T*P/G is a Poisson manifold. We will determine the Poisson bracket on the reduced Poisson manifold T*P/G, and its symplectic leaves. © 1999 American Institute of Physics.

Notes: Cauchy analysis of the linearized field equations of the skew sector of the massive nonsymmetric gravitational theory shows that small perturbations give rise to bounded accelerations thereby ensuring good asymptotic behavior for the skew part of the fundamental tensor. © 1999 American Institute of Physics.

Notes: It is shown that the first-order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-Hermitian metric on a complex manifold satisfies the Kähler condition on the same manifold treated as a real manifold if and only if the metric is the real part of a holomorphic metric. A characterization of anti-Kähler Einstein manifolds and almost-product Einstein manifolds is obtained. Examples of such manifolds are considered. © 1999 American Institute of Physics.

Notes: We obtain a class of exact solutions representing null particles moving in three-dimensional (anti-) de Sitter spaces by boosting the corresponding static point source solutions given by Deser and Jackiw. In de Sitter space the resulting solution describes two null particles moving on the (circular) cosmological horizon, while in anti-de Sitter space it describes a single null particle propagating from one side of the universe to the other. We also boost the Bañados–Teitelboim–Zanelli black hole solution to the ultrarelativistic limit and obtain the solution for a spinning null particle moving in anti-de Sitter space. We find that the ultrarelativistic geometry of the black hole is exactly the same as that resulting from boosting the Deser–Jackiw solution when the angular momentum of the hole vanishes. A general class of solutions is also obtained which represents several null particles propagating in the Deser–Jackiw background. The differences between the three-dimensional and four-dimensional cases are also discussed. © 1999 American Institute of Physics.

Notes: Building on the results of previous work [M. A. Clayton, "Canonical general relativity: Diffeomorphism constraints and spatial frame transformations," J. Math. Phys. 39, 3805–3816 (1998)], we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads naturally to canonical vierbein general relativity has the extrinsic curvature of the Cauchy surface represented by gravitational as well as nongravitational degrees of freedom. Nevertheless the metric compatibility conditions are undisturbed, and this apparent derivative-coupling is seen to be an effect of working with (possibly orthonormal) linear frames. The formalism is adapted to consider a Dirac Fermion, where we find that a milder form of this apparent derivative-coupling appears. © 1999 American Institute of Physics.

Notes: All of the homogeneous Lorentzian structures on the oscillator group equipped with a bi-invariant Lorentzian metric, and then the associated reductive pairs, are obtained. Some of them are solutions of the Einstein–Yang–Mills equations. © 1999 American Institute of Physics.

Notes: A study of radial conformal Killing fields (RCKF) in Minkowski space–time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed. © 1999 American Institute of Physics.

Notes: We extend Witten's proof on positive mass conjecture to five-dimensional Lorentzian manifolds with a rigorous treatment in mathematics. © 1999 American Institute of Physics.