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

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.

arXiv comment28 pages, submitted to Phys.Rev.D

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• Spontaneous magnetization of a vacuum in the hot Universe and intergalactic magnetic fields
• Groundstate projection of the charged SU(2) polarization tensor in a chromomagnetic background field
• Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe
• Lower bound on the magnetic field strength in the hot universe