Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the hard thermal loop approximation - art. no. 025015

We evaluate the fermion-photon vertex in QED at the one loop level in the h ard thermal loop approximation and write it in covariant form. The complete vertex can be expanded in terms of 32 basis vectors. As is well known, the fermion-photon vertex and the fermion propagator are related through a War d-Takahashi identity (WTI). This relation splits the vertex into two parts: longitudinal (Gamma (L)) and transverse (Gamma (T)) Gamma (L) is fixed by the WTI. The description of the longitudinal part consumes 8 of the basis v ectors. The remaining piece Gamma (T) is then written in terms of 24 spin a mplitudes. Extending the work of Ball and Chiu and Kizilersu and co-workers , we propose a set of basis vectors T-i(u)(P-1,P-2) at finite temperature s uch that each of these is transverse to the photon four-momentum and also s atisfies T-i(u)(P,P) = 0, in accordance with the Ward identity, with their corresponding coefficients being free of kinematic singularities. This basi s reduces to the form proposed by Kizilersu and co-workers at zero temperat ure. We also evaluate explicitly the coefficient of each of these vectors a t the above-mentioned level of approximation.