Retarded/Advanced Correlation Functions and Soft Photon Production in the Hard Loop Approximation

TL;DR

This paper employs real-time field theory formalism to analyze correlation functions and soft photon production in QED, deriving the hard loop expansion and identifying divergences in soft photon emission.

Contribution

It introduces a formalism for calculating correlation functions and soft photon production in QED using the retarded/advanced approach, including the derivation of the hard loop expansion.

Findings

Derived a general expression for the imaginary part of the two-point correlation function.

Obtained the hard loop expansion in the context of QED.

Identified divergences in the soft fermion loop contribution to soft photon production.

Abstract

We apply the retarded/advanced formalism of real time field theory to the QED or QED like case. We obtain a general expression for the imaginary part of the two-point correlation function in terms of discontinuities. The hard loop expansion is derived. The formalism is used to extract the divergent part of the soft fermion loop contribution to the real soft photon production.