On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

Details On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

1998-01-03

arxiv.org/abs/hep-th/9801006v1

J.Math.Phys. 39 (1998) 4492-4498

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, Latex; email: anmitra@csec.ernet.in

Scientific paper

10.1063/1.532521

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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