On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions
High Energy Physics - Theory
2009-10-31 v1
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.
Cite
@article{arxiv.hep-th/9801006,
title = {On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions},
author = {A. N. Mitra and R. Ramanathan},
journal= {arXiv preprint arXiv:hep-th/9801006},
year = {2009}
}
Comments
9 pages, Latex; email: anmitra@csec.ernet.in