Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity

TL;DR

This paper investigates unitarity in time-ordered perturbation theory on noncommutative spacetime, demonstrating that unitarity holds if the interaction Lagrangian is Hermitian, clarifying the role of Hermiticity in this framework.

Contribution

It clarifies the conditions under which unitarity is preserved in perturbative noncommutative field theory, emphasizing the importance of Hermitian interaction Lagrangians.

Findings

Unitarity is preserved with Hermitian interaction Lagrangian.

Distinction between Hermiticity of Lagrangian and action is justified.

Framework consistency for perturbative NC field theory is established.

Abstract

We examine the unitarity issue in the recently proposed time-ordered perturbation theory on noncommutative (NC) spacetime. We show that unitarity is preserved as long as the interaction Lagrangian is explicitly Hermitian. We explain why it makes sense to distinguish the Hermiticity of the Lagrangian from that of the action in perturbative NC field theory and how this requirement fits in the framework.