Klein-Gordon and Dirac Equations with Thermodynamic Quantities

TL;DR

This paper analyzes thermodynamic quantities like free energy and specific heat for Klein-Gordon and Dirac equations with specific potentials, providing analytical high-temperature results and exploring the effects of scalar and vector potentials.

Contribution

It offers new analytical expressions for thermodynamic functions of relativistic quantum equations with particular potentials, focusing on high-temperature behavior.

Findings

Analytical high-temperature thermodynamic functions derived.

Effects of Lorentz scalar and vector potentials analyzed.

Positive spectrum contribution considered in partition functions.

Abstract

We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein-Gordon, and Dirac equations. Our analyze includes two main subsections: ($i$) statistical functions for the Klein-Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts ($ii$) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong ($A \gg 1$). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.