In this work, we consider the light front quantum electrodynamics in ($3+1$) dimensions and evaluate the photon polarization tensor at one loop for both zero and finite temperatures. In the first case, we apply the dimensional regularization method to extract the finite contribution and find the transverse structure for the amplitude in terms of the light front coordinates. The result agrees with one-loop covariant calculation. For the thermal corrections, we generalize the hard thermal loop approximation to the light front and calculate the dominant temperature contribution to the polarization tensor, consistent with the Ward identity. In both zero as well as finite temperature calculations, we use the oblique light front coordinates.

• Received 11 February 2012

DOI:https://doi.org/10.1103/PhysRevD.85.105021