Gluon polarization tensor in color magnetic background

In SU(2) gluodynamics we calculate the gluon polarization tensor in an Abelian homogeneous magnetic field in one-loop order in the Lorentz background field gauge. It turned out to be non-transversal and consisting of ten tensor structures and corresponding form factors - four in color neutral and six in color charged sector. Seven tensor structures are transversal, three are not. The non-transversal parts are obtained by explicit calculation. We represent the form factors in terms of double parametric integrals which can be computed numerically. Some examples are provided and possible applications are discussed. Received: 23 August 2005, Published online: 21 November 2005 PACS: 11.15.-q, 12.38.-t