A Note on Unitarity of Non-Relativistic Non-Commutative Theories

TL;DR

This paper investigates the unitarity properties of non-relativistic non-commutative scalar field theories, revealing that electric backgrounds break unitarity and cannot be restored, indicating limitations in embedding these models into string theory.

Contribution

It provides a detailed analysis of unitarity in non-relativistic non-commutative theories, highlighting differences from relativistic cases and the inability to restore unitarity with additional states.

Findings

Electric backgrounds spoil unitarity

Magnetic backgrounds do not affect unitarity

Unitarity cannot be restored by adding states

Abstract

We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be restored (at least at the level of one-to-one scattering amplitude) by adding new states to the theory. This is a signal that the model cannot be embedded in a natural way in string theory.