On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions
نویسندگان
چکیده
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. PACS: 05.60.+w ; 03.65.Ca ; 11.10.Qr ; 11.40.-q ∗e.mail: (1) [email protected](subj:a.n.mitra); (2) [email protected]
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