A simple method to obtain the all order quantum corrected Bose-Einstein distribution

TL;DR

This paper presents a straightforward perturbative method to derive the all-order quantum corrected Bose-Einstein distribution from the Wigner equation, useful for studying bosons and condensates at finite temperatures.

Contribution

The paper introduces a simple perturbative approach to obtain quantum corrected Bose-Einstein distributions directly from the Wigner equation, extending to Fermi distributions.

Findings

Derived the quantum corrected Bose-Einstein distribution as a solution to the Wigner equation.

Applied the method to calculate boson number density at finite temperature.

Potentially applicable to study properties of bosons and Bose condensates.

Abstract

A simple method has been introduced to derive the all order quantum corrected Bose-Einstein distribution as the solution of the Wigner equation. The process is a perturbative one where the Bose-Einstein distribution has been taken as the unperturbed solution. This solution has been applied to calculate the number density of the bosons at finite temperature. The study may be important to investigate the properties of bosons and bose condensates at finite temperature. This process can also be applied to obtain the quantum corrected Fermi distribution.