Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory

TL;DR

This paper demonstrates that Lorentz-invariant non-commutative  theory at one-loop level is finite and unitary after subtraction, resolving issues present in Lorentz-non-invariant formulations.

Contribution

It shows that Lorentz-invariant non-commutative  theory avoids unitarity and divergence problems found in Lorentz-non-invariant models.

Findings

One-loop two-point amplitude is finite after subtraction.

The theory satisfies the usual cutting rule.

Unitarity problem is eliminated in the considered approximation.

Abstract

It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant} non-commutative (NC) $\phi^3$ theory is finite after subtraction in the commutative limit and satisfies the usual cutting rule, thereby eliminating the unitarity problem in Lorentz-non-invariant NC field theory in the approximation considered.