Unitarity-Cuts, Stokes' Theorem and Berry's Phase

TL;DR

This paper introduces a novel approach to compute two-particle unitarity cuts in scattering amplitudes using Stokes' Theorem, linking the Optical Theorem to Berry's Phase and interpreting the imaginary part of one-loop amplitudes as a flux of a complex 2-form.

Contribution

It establishes a new connection between unitarity cuts, Stokes' Theorem, and Berry's Phase, providing a geometric interpretation of the imaginary parts of one-loop amplitudes.

Findings

Efficient computation of unitarity cuts via Stokes' Theorem.

Relation between the Optical Theorem and Berry's Phase.

Imaginary parts of one-loop amplitudes as flux of a complex 2-form.

Abstract

Two-particle unitarity-cuts of scattering amplitudes can be efficiently computed by applying Stokes' Theorem, in the fashion of the Generalised Cauchy Theorem. Consequently, the Optical Theorem can be related to the Berry Phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.