Momentum expansions in finite-density perturbative calculations

TL;DR

This paper investigates infrared divergences and integration ambiguities in finite-density quantum field theory, proposing novel complex-valued integral extensions and representations to resolve these issues in fermionic loop calculations.

Contribution

It introduces new complex-valued extensions for bubble Feynman integrals and a representation that avoids integration order ambiguities in finite-density perturbative calculations.

Findings

Identified mechanisms causing discrepancies in momentum expansions

Developed a representation to eliminate integration ambiguities

Outlined classes of integrals unaffected by external momentum issues

Abstract

Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to integration order dependent results are even further pronounced in the presence of additional scales such as external momenta. This plays a noticeable role in systems featuring fermionic degrees of freedom such as cold Quantum Chromodynamics, where loop integrals are complexified by chemical potential(s). Working in the limit of vanishing temperature, we utilize novel complex-valued extensions to bubble Feynman integrals and study momentum expansions of fermionic loop integrals. The expansions are then used to illustrate the mechanisms of manifested discrepancies between orders of integration, associated with the residue theorem. Finally, we address the issues by introducing a representation avoiding the observed ambiguity and briefly overview classes of integrals insensitive to problems from external momenta.