Failure of microcausality in quantum field theory on noncommutative spacetime

TL;DR

This paper demonstrates that quantum field theory on noncommutative spacetime violates microcausality, challenging fundamental assumptions about causality in such theories, even when time-space noncommutativity is absent.

Contribution

It shows that noncommutative quantum field theories inherently fail to satisfy microcausality, extending the issue to general fields and observables.

Findings

Star commutator fails to vanish at equal times

Microcausality is violated at spacelike separation

Failure persists even when i=0

Abstract

The star commutator of $:\phi(x) \star \phi(x):$ with $:\phi(y) \star \phi(y):$ fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which $\theta^{0i}=0$. The failure to obey microcausality for this sample observable implies that this form of noncommutative field theory fails to obey microcausality in general. This result also holds for general fields and observables. We discuss possible responses to this problem.