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Deformation Quantization: Quantum Mechanics Lives and Works in Phase-Space

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arxiv hep-th/0110114 v3 pith:EFWE4PBX submitted 2001-10-12 hep-th quant-ph

Cosmas K Zachos This is my paper · ORCID
classification hep-thquant-ph
keywords quantumformulationphase-spacemechanicsspaceworksaccommodatingalternative
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Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" discussions; semiclassical limits. It is also of importance in signal processing. Nevertheless, a remarkable aspect of its internal logic, pioneered by Moyal, has only emerged in the last quarter-century: It furnishes a third, alternative, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations. In this logically complete and self-standing formulation, one need not choose sides--coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle. This is an introductory overview of the formulation with simple illustrations.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Phase space quantization of anisotropic cosmologies: Taub and Kantowski-Sachs models

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Phase space quantization via Wigner distributions and Moyal product for Taub and Kantowski-Sachs models recovers modified Bessel function wave functions without factor ordering ambiguities.

  2. The Jaynes-Cummings model in Phase Space Quantum Mechanics

    quant-ph 2025-06 reject novelty 3.0 of 10

    A hybrid qubit-field Wigner function for the Jaynes-Cummings model is constructed, reproducing standard Rabi and inversion results, but the one-mode Wigner function and the reduced-field purity formula are incorrect a...

  3. The Feynman-Kac formula in deformation quantization

    math-ph 2025-02 conditional novelty 3.0 of 10

    The ground state energy of a quantum system is extracted from the large imaginary-time limit of the phase space integral of the star exponential of the Hamiltonian, a reformulation of the trace formula.

  4. Wigner function under changes of reference frames

    math-ph 2024-11 conditional novelty 3.0 of 10

    Under unitary reference-frame changes that map position to X(x) and momentum to P(p), the Wigner function transforms by an explicit integral formula, reducing to W(X,P) in the affine examples shown.

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