Perturbation theory in (2,2) signature

TL;DR

This paper introduces a method for analytically continuing scalar Feynman diagrams from Minkowski to a (2,2) signature, simplifying their evaluation by reducing integrals through contour deformation and pole analysis.

Contribution

It presents a novel analytic continuation technique for scalar diagrams in four dimensions, enabling simplified integral representations in a (2,2) signature.

Findings

Contour deformation preserves momentum dependence.

Two integrals per loop can be expressed via simple poles.

Any ultraviolet-finite scalar diagram can be represented as a sum of terms with reduced integrals.

Abstract

We identify a natural analytic continuation in four dimensions from Minkowski signature to a signature with two time-like momentum components. For two, three and four-point diagrams at fixed external momenta, this continuation can be implemented as a countour deformation that leaves dependence on the momenta unchanged. For arbitrary ultraviolet-finite scalar diagrams it is possible to do two integrals per loop in terms of simple poles in the new signature. This results in a representation of any such diagram as a sum of terms, each with two remaining integrals per loop.