Neutral gluon polarization tensor in color magnetic background at finite temperature

In the framework of SU(2) gluodynamics, we derive the tensor structure of the neutral gluon polarization tensor in an Abelian homogeneous magnetic field at finite temperature and calculate it in one-loop approximation in the Lorentz background field gauge. The imaginary time formalism and the Schwinger operator method are used. The latter is extended to the finite temperature case. The polarization tensor turns out to be non transversal. It can be written as a sum of ten tensor structures with corresponding form factors. Seven tensor structures are transversal, three are not. We represent the form factors in terms of double parametric integrals and the temperature sum which can be computed numerically. As applications we calculate the Debye mass and the magnetic mass of neutral gluons in the background field at high temperature. A comparison with the results of other authors is done.