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  • 1
    Electronic Resource
    Electronic Resource
    Geometric quantization: Modular reduction theory and coherent states (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2936-2943 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The natural role played by coherent states in the geometric quantization program is brought out by studying the mathematical equivalence between two physical interpretations that have recently been proposed for this program. These interpretations are based, respectively, on the modular algebra structure of prequantization, and the reproducing kernel structure of phase space quantization. The arguments are presented in this paper for the particular case where the phase space of the system considered is the cotangent bundle T*M of a homogeneous manifold M, and for didactic reasons, the latter is taken to be a real vector space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527271
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  • 2
    Electronic Resource
    Electronic Resource
    New classical properties of quantum coherent states (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2731-2737 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527295
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  • 3
    Electronic Resource
    Electronic Resource
    Comments on a recent paper by S. Adler on projective group representations in quaternionic Hilbert spaces (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6582-6585 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A version of Schur's lemma is proven that elucidates some issues raised by that paper. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531793
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  • 4
    Electronic Resource
    Electronic Resource
    Modular algebras in geometric quantization (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6237-6243 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Presented here is a discussion on the connection between geometric quantization and algebraic quantization. The former procedure relies on a construction of unitary irreducible representations that starts from co-adjoint orbits and uses polarizations, while the latter depends on the purely algebraic characterization of unitary irreducible representations, which is based on central decompositions of von Neumann algebras in involutive duality, and their decompositions in terms of maximal Abelian subalgebras. Intermediate stages of these two quantization methods turn out to be complementary, leading thus to a new characterization of the so-called discrete series representations. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530672
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  • 5
    Electronic Resource
    Electronic Resource
    GeneralizedK-flows (1976)
    Springer
    Communications in mathematical physics 49 (1976), S. 191-215 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The classical concept ofK-flow is generalized to cover situations encountered in non-equilibrium quantum statistical mechanics. The ergodic properties of generalizedK-flows are discussed. Several non-isomorphic examples are constructed, which differ already in the type (II1, IIIλ, and III1) of the factor on which they are defined. In particular, generalized factorK-flows with dynamical entropy either zero (singularK-flows) or infinite (special non-abelianK-flows) are constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608727
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  • 6
    Electronic Resource
    Electronic Resource
    Relativistic particle scattering (1985)
    Springer
    Communications in mathematical physics 101 (1985), S. 539-557 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In the presence of competing relativistic formalisms for interacting particle dynamics, a model-independent axiomatic approach is proposed for the study of the following asymptotic aspects of relativistic classical particle dynamics: the definition of the scattering operator, scattering angle and time-delay, and the specification of a general functional interdependence between the objects so defined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01210744
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  • 7
    Electronic Resource
    Electronic Resource
    Positivity of the K-entropy on non-abelian K-flows (1974)
    Springer
    Probability theory and related fields 29 (1974), S. 241-252 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A non-commutative extension of certain aspects of classical probability theory is presented in such a manner that the notion of Kolmogorov entropy can be extended to a large class of non-classical dynamical systems. In particular, the generalized K-entropy so defined is shown to be strictly positive on the class of non-abelian K-flows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536283
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  • 8
    Electronic Resource
    Electronic Resource
    Geometric dequantization and the correspondence problem (1983)
    Springer
    International journal of theoretical physics 22 (1983), S. 397-420 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract On the way to settle a conjecture proposed by Mackey, we first present in detail a complete solution to the correspondence problem for systems whose configuration space isR n . We then indicate how this can be considered as a first step in the elaboration of a geometric dequantization program which would extend the results to more general manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083286
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  • 9
    Electronic Resource
    Electronic Resource
    Prequantization and KMS structures (1981)
    Springer
    International journal of theoretical physics 20 (1981), S. 891-904 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The properties of the representations of the canonical commutation relations, obtained in the prequantization program, are investigated with special attention to the relevance of the KMS structures in this context. In particular, we show how these structures provide a natural way to pass from the prequantization representation of the CCR to the Schrödinger representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00670552
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  • 10
    Electronic Resource
    Electronic Resource
    On the standard form of the Bloch equation (1979)
    Springer
    Letters in mathematical physics 3 (1979), S. 113-116 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The requirement is often made in non-equilibrium statistical mechanics that a transport equation should be derived as that which governs the subdynamics relative to a (small) part of a (large) conservative dynamical system close to equilibrium. We show that such a requirement on the Markovian relaxation of a 1/2-spin imposes that this process be described by a Bloch equation of a very specific form, which we call standard. We show that this reduced dynamics is quasi-free if, and only if, the relaxation time is maximally anisotropic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00400065
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