Unitarity and Asymptotic Behavior of Amplitudes in Non-Anticommutative Quantum Field Theory

TL;DR

This paper investigates unitarity and high-energy behavior of scattering amplitudes in non-anticommutative quantum field theory, demonstrating the validity of Cutkosky rules and regularity at high energies under specific conditions.

Contribution

It shows that unitarity can be maintained in non-anticommutative quantum field theory and that amplitudes behave regularly at high energies with space-space non-anticommutativity.

Findings

Cutkosky rules hold in Euclidean space

Unitarity can be satisfied without unphysical singularities

High energy amplitudes are regular with space-space non-anticommutativity

Abstract

The unitarity condition for scattering amplitudes in a non-anticommutative quantum field theory is investigated. The Cutkosky rules are shown to hold for Feynman diagrams in Euclidean momentum space and unitarity of amplitudes can be satisfied. An analytic continuation of the diagrams to physical Minkowski spacetime can be performed without invoking unphysical singularities in amplitudes. The high energy behavior of amplitudes is found to be regular at infinity provided that only space-space non-anticommutativity is allowed.