  Based on transversality condition of gauge boson self-energy we have
systematically constructed the general structure of the gauge boson two-point
functions using four linearly independent basis tensors in presence of a
nontrivial background, i.e., hot magnetized material medium. The hard thermal
loop approximation has been used for the heat bath to compute various form
factors associated with the gauge boson's two point functions both in strong
and weak field approximation. We have also analyzed the dispersion of a gauge
boson (e.g., gluon) using the effective propagator both in strong and weak
magnetic field approximation. The formalism is also applicable to QED. The
presence of only thermal background leads to a longitudinal (plasmon) mode and
a two-fold degenerate transverse mode. In presence of a hot magnetized
background medium the degeneracy of the two transverse modes is lifted and one
gets three quasiparticle modes. In weak field approximation one gets two
transverse modes and one plasmon mode. On the other hand, in strong field
approximation also one gets the three modes in Lowest Landau Level. The general
structure of two-point function may be useful for computing the thermo-magnetic
correction of various quantities associated with a gauge boson.
