Two-Loop Self-Energy and Multiple Scattering at Finite Temperature

TL;DR

This paper explicitly calculates one- and two-loop self-energies for a scalar field at finite temperature, illustrating the link between multi-loop diagrams and multiple scattering phenomena in a medium.

Contribution

It provides explicit calculations of self-energies and demonstrates how to sum complex diagram sets, connecting multi-loop diagrams with multiple scattering effects.

Findings

Explicit expressions for one- and two-loop self-energies.

Summation of ring/daisy and necklace diagrams.

Illustration of the connection between multi-loop diagrams and scattering.

Abstract

One and two loop self-energies are worked out explicitly for a heavy scalar field interacting weakly with a light self-interacting scalar field at finite temperature. The ring/daisy diagrams and a set of necklace diagrams can be summed simultaneously. This simple model serves to illustrate the connection between multi-loop self-energy diagrams and multiple scattering in a medium.