1998/01/03 by A. N. Mitra, Ravishankar Ramanathan, R. Ramanathan · 1 citation
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Covariant transformation #Dirac equation #Flow (mathematics) #Formalism (music) #Fourier transform #Lorentz transformation #Mathematical physics #Mathematics #Mechanics #Physics #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum dynamics #Quantum mechanics #Relativistic quantum mechanics #Statistical mechanics #Wigner distribution function #hep-th
paper · pdf · doi:10.1063/1.532521
published in Journal of Mathematical Physics 39(9), 4492-4498 (American Institute of Physics) · 9 pages, Latex; email: [email protected]
arxiv created 1998/01/03 · openalex publication_date 1998/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.