Spin-1/2 particles in Phase space: Casimir effect and Stefan-Boltzmann law at finite temperature

TL;DR

This paper explores the behavior of spin-1/2 particles in phase space, deriving thermodynamic laws and effects like Stefan-Boltzmann and Casimir at finite temperatures, and compares these with standard quantum mechanics results.

Contribution

It introduces a phase space formulation for Dirac fields, calculates finite temperature effects, and compares phase space results with traditional quantum mechanics.

Findings

Stefan-Boltzmann law established for Dirac field in phase space

Casimir effect computed at zero and finite temperature

Comparison with standard quantum mechanics shows consistent results

Abstract

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.