Aspects of perturbative unitarity

TL;DR

This paper revisits perturbative unitarity in quantum field theory, providing a simplified proof for gauge theories and extending it to quantum gravity, while clarifying assumptions and gauge choices involved.

Contribution

It offers a new, simpler proof of perturbative unitarity in gauge theories and generalizes it to quantum gravity using a special gauge that interpolates between Feynman and Coulomb gauges.

Findings

Simplified proof of perturbative unitarity in gauge theories.

Extension of unitarity proof to quantum gravity in various dimensions.

Identification of assumptions leading to unitarity equations.

Abstract

We reconsider perturbative unitarity in quantum field theory and upgrade several arguments and results. The minimum assumptions that lead to the largest time equation, the cutting equations and the unitarity equation are identified. Using this knowledge and a special gauge, we give a new, simpler proof of perturbative unitarity in gauge theories and generalize it to quantum gravity, in four and higher dimensions. The special gauge interpolates between the Feynman gauge and the Coulomb gauge without double poles. When the Coulomb limit is approached, the unphysical particles drop out of the cuts and the cutting equations are consistently projected onto the physical subspace. The proof does not extend to nonlocal quantum field theories of gauge fields and gravity, whose unitarity remains uncertain.