On simulating Liouvillian flow from quantum mechanics via Wigner functions

Mitra, A. N. ; Ramanathan, R. (1998) On simulating Liouvillian flow from quantum mechanics via Wigner functions Journal of Mathematical Physics, 39 (9). pp. 4492-4498. ISSN 0022-2488

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Official URL: http://jmp.aip.org/resource/1/jmapaq/v39/i9/p4492_...

Related URL: http://dx.doi.org/10.1063/1.532521

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 β-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.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Quantum Theory; Probability; Classical Mechanics; Dirac Equation; Relativistic Quantum Field Theory; Current Algebra; Fourier Transforms; Matrix Algebra; Conservation Laws
ID Code:90189
Deposited On:07 May 2012 13:13
Last Modified:19 May 2016 04:28

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