Classification of higher order diagrams in non-equilibrium theory, and the removal of pinch singularities

TL;DR

This paper analyzes higher order diagrams in non-equilibrium quantum field theory, showing that pinch singularities do not occur at the two-loop level in equilibrium and near-equilibrium conditions, and clarifies the role of non-collisional terms.

Contribution

It classifies higher order diagrams in non-equilibrium theory and demonstrates the absence of pinch singularities at the two-loop level in equilibrium and near-equilibrium states.

Findings

Most non-collisional terms contribute to line renormalization.

Pinch singularities do not arise at two loops in equilibrium.

Remaining non-physical terms vanish explicitly.

Abstract

The non-equilibrium two loop self-energy is reexamined in the framework of a scalar quark and gluon model, with specific attention to terms which do not give rise to the standard two -> two particle collisional terms in the semi-classical Boltzmann equation. It is shown that most of these terms contribute to renormalization of component lines at a lower level, rendering the theory correct to (gm)^4. This result can be generalized to a higher number of loops. The remaining terms, which do not fall into any physical category, are shown explicitly to vanish. We then examine the possibility that pinch singularities could arise in this theory, and demonstrate that this is not so for the case of equilibrium and small deviations from equilibrium, at the two loop level.