Renormalization of number density in nonequilibrium quantum-field theory and absence of pinch singularities

TL;DR

This paper introduces a renormalization scheme for particle-number density in nonequilibrium quantum-field theory, simplifying calculations and eliminating pinch singularities by using renormalized distribution functions.

Contribution

It proposes a novel perturbation scheme based on renormalized distribution functions, aligning nonequilibrium calculations with equilibrium thermal field theory and removing pinch singularities.

Findings

Amplitudes and reaction rates are free from pinch singularities.

The structure of the scheme mirrors that of equilibrium thermal field theory.

The approach simplifies nonequilibrium quantum-field calculations.

Abstract

Through introducing a notion of renormalization of particle-number density, a simple perturbation scheme of nonequilibrium quantum-field theory is proposed. In terms of the renormalized particle-distribution functions, which characterize the system, the structure of the scheme (and then also the structure of amplitudes and reaction rates) are the same as in the equilibrium thermal field theory. Then, as an obvious consequence, the amplitudes and reaction rates computed in this scheme are free from pinch singularities due to multiple products of $\delta$-functions, which inevitably present in traditional perturbation scheme.