Spin-1/2 Particles in Phase Space: Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

R G G Amorim,S C Ulhoa,F C Khanna,A F Santos,J S Da Cruz Filho,Michele Arzano

doi:10.1155/2020/7032834

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.

Highlights

The Wigner function formalism [1, 2] and noncommutative geometry [3] play a fundamental role in the study of phase space quantum mechanics
Our goal is to explore the quasiprobability amplitude to study the effect of temperature using Thermo Field Dynamics (TFD) formalism [7,8,9,10,11,12,13] in a system for spin-1/2 particles
The TFD results are obtained by using the temperature effects in the Dirac propagator

Summary

Introduction

The Wigner function formalism [1, 2] and noncommutative geometry [3] play a fundamental role in the study of phase space quantum mechanics. The Wigner formalism enables a quantum operator, A, defined in the Hilbert space, S, to have an equivalent function of the type awðq, pÞ, in phase space Γ, using the Moyal-product or star-product (å). Our goal is to explore the quasiprobability amplitude to study the effect of temperature using Thermo Field Dynamics (TFD) formalism [7,8,9,10,11,12,13] in a system for spin-1/2 particles The principles of this theory are the duplication of the Fock space using the Bogoliubov transformations. It should be noted that due to the dependence on the Dirac matrices, the Green’s function has matrix properties itself

Thermo Field Dynamics Formalism

Stefan-Boltzmann Law and Casimir Effect for the Dirac Field in Phase Space

Conclusion