2025/05/06 by M. J. Everitt, Everitt, Mark J. · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics
paper · pdf · doi:10.48550/arxiv.2505.03551
openalex publication_date 2025/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here we argue that spinor structure arises naturally if relativistic statistical mechanics is formulated directly on phase spacetime. Requiring a first-order phase-spacetime description that retains both mass-shell branches leads to a Clifford factorisation of the relativistic constraint and hence to a 4×4 spinor-matrix distribution function. We show that deformation quantisation leads to a phase-space formulation of spin quantum mechanics. We argue that projection onto positive- and negative-energy sectors recovers the standard relativistic classical transport equations in the appropriate scalar limits, while the corresponding left- and right- stargenvalue equations reproduce the constraint structure of the Dirac-Wigner formulation. The result is a phase-space route from relativistic statistical mechanics to spinor quantum mechanics, in which spin algebra emerges as the internal structure required by any relativistic statistical theory containing both mass-shell branches and the dimensions of angular momentum from quantum non-locality.