Forward scattering amplitudes and the thermal operator representation

TL;DR

This paper develops a systematic forward scattering framework for retarded amplitudes at zero and finite temperatures, simplifying calculations and relating thermal and zero-temperature field theory amplitudes.

Contribution

It introduces a comprehensive method to derive finite temperature retarded amplitudes from zero temperature ones using the thermal operator, enhancing computational efficiency.

Findings

Derived the finite temperature retarded gluon self-energy in the hard thermal loop approximation.

Established a graphical and calculational relation between zero and finite temperature amplitudes.

Provided a systematic all-orders development of the forward scattering description.

Abstract

We develop systematically to all orders the forward scattering description for retarded amplitudes in field theories at zero temperature. Subsequently, through the application of the thermal operator, we establish the forward scattering description at finite temperature. We argue that, beyond providing a graphical relation between the zero temperature and the finite temperature amplitudes, this method is calculationally quite useful. As an example, we derive the important features of the one loop retarded gluon self-energy in the hard thermal loop approximation from the corresponding properties of the zero temperature amplitude.