Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation

Details Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation Longitudinal and transverse fermion-boson vertex in QED at finite temperature in the HTL approximation

2001-03-02

arxiv.org/abs/hep-ph/0103030v1

Phys.Rev. D64 (2001) 025015

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, uses RevTeX

Scientific paper

10.1103/PhysRevD.64.025015

We evaluate the fermion-photon vertex in QED at the one loop level in Hard 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 Ward-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 vectors. The remaining piece Gamma_T is then written in terms of 24 spin amplitudes. Extending the work of Ball and Chiu and Kizilersu et. al., we propose a set of basis vectors T^mu_i(P_1,P_2) at finite temperature such that each of these is transverse to the photon four-momentum and also satisfies T^mu_i(P,P)=0, in accordance with the Ward Identity, with their corresponding coefficients being free of kinematic singularities. This basis reduces to the form proposed by Kizilersu et. al. at zero temperature. We also evaluate explicitly the coefficient of each of these vectors at the above-mentioned level of approximation.

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