Unitarity-Cuts and Berry's Phase

TL;DR

This paper links the computation of unitarity-cuts in scattering amplitudes to Berry's Phase, revealing a geometric interpretation of the imaginary parts of one-loop Feynman amplitudes as fluxes of complex 2-forms.

Contribution

It introduces a novel geometric perspective connecting unitarity-cuts and Berry's Phase in quantum field theory.

Findings

Unitarity-cuts can be computed via Stokes' Theorem.

Imaginary parts of one-loop amplitudes relate to fluxes of complex 2-forms.

Optical Theorem is interpreted through Berry's Phase.

Abstract

Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes' Theorem, we relate the Optical Theorem 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.