Four-Point Spectral Functions and Ward Identities in Hot QED

TL;DR

This paper derives spectral representations for 4-point functions at finite temperature in hot QED, explicitly calculates them in the hard thermal loop approximation, and explores Ward identities and their implications.

Contribution

It introduces a real-time spectral representation for 4-point functions and explicitly computes these in hot QED, linking real-time and imaginary-time formalisms.

Findings

Spectral representations involve five real spectral densities.

Ward identities are derived for 1-loop 3- and 4-point functions.

Results are compared with previous imaginary-time formalism studies.

Abstract

We derive spectral representations for the different components of the 4-point function at finite temperature in the real time formalism in terms of five real spectral densities. We explicitly calculate all these functions in QED in the hard thermal loop approximation. The Ward identities obeyed by the 1-loop 3- and 4-point functions in real time and their spectral functions are derived. We compare our results with those derived previously in the imaginary-time formalism for retarded functions in hot QCD, and we discuss the generalization of our results to non-equilibrium situations.