Noncommutative Dipole Field Theories And Unitarity

TL;DR

This paper investigates unitarity violations in dipole field theories with space-time noncommutativity, demonstrating that certain models and quantum systems exhibit violations of fundamental unitarity principles at the quantum level.

Contribution

It extends previous work on noncommutative field theories by analyzing unitarity violations specifically in dipole field theories with timelike dipole vectors.

Findings

1-loop amplitudes violate the optical theorem in certain dipole theories

Quantum systems with nonlocal potentials also show unitarity violation

Unitarity violations are linked to space-time noncommutativity in these models

Abstract

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.