  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.
