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arXiv · hep-th/9801006

On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

A. N. Mitra·R. Ramanathan
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Abstract

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer- Duffin beta-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard `trace' techniques. The results are compared with a recent derivation due to Bosanac.

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A. N. Mitra, R. Ramanathan. 1998-01-03. On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions. https://doi.org/10.1063/1.532521

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