Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential

TL;DR

This paper develops a thermal operator approach to derive cutting rules at finite temperature and chemical potential in scalar field theories, enabling calculations of self-energy and dispersion relations in thermal environments.

Contribution

It introduces a thermal operator method to extend zero-temperature cutting rules to finite temperature and chemical potential, with an algebraic proof of the largest time equation.

Findings

Derived finite-temperature cutting rules from zero-temperature rules.

Calculated the imaginary part of the one-loop retarded self-energy.

Demonstrated how to compute dispersion relations and physical self-energy.

Abstract

In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal operator. We give an alternative algebraic proof of the largest time equation which brings out the underlying physics of such a relation. As an application of the cutting description, we calculate the imaginary part of the one loop retarded self-energy at zero/finite temperature and finite chemical potential and show how this description can be used to calculate the dispersion relation as well as the full physical self-energy of thermal particles.