Polarization tensor of charged gluons in color magnetic background field at finite temperature

TL;DR

This paper computes the polarization tensor of charged gluons in a magnetic background at finite temperature, revealing detailed tensor structures and nontransversal components using advanced mathematical techniques.

Contribution

It provides a comprehensive calculation of the polarization tensor's tensor structures and form factors for charged gluons in a magnetic field at finite temperature, including nontransversal parts.

Findings

Identified ten independent tensor structures.

Derived explicit form factors as double parametric integrals.

Found that the polarization tensor is not fully transversal.

Abstract

We calculate the polarization tensor of charged gluons in a Abelian homogeneous magnetic background field at finite temperature in one loop order Lorentz background field gauge in full generality. Thereby we first determine the ten independent tensor structures. For the calculation of the corresponding form factors we use the Schwinger representation and represent form factors as double parametric integrals and a sum resulting from the Matsubara formalism used. The integrands are given explicitly in terms of hyperbolic trigonometric functions. Like in the case of neutral gluons, the polarization tensor is not transversal. Out of the tensor structures, seven are transversal and three are not. The nontransversal part follows explicitly from our calculations.