Microcausality of spin-induced noncommutative theories

TL;DR

This paper investigates the microcausality property in quantum field theories on spin-induced noncommutative spacetime, finding that microcausality generally fails, which questions the compatibility of Lorentz covariance with causality.

Contribution

It demonstrates that Lorentz covariance does not guarantee microcausality in spin-induced noncommutative quantum field theories, providing insights into the relationship between noncommutative spacetime and causality.

Findings

Microcausality is generally violated at spacelike separations.

Lorentz covariance does not ensure microcausality in these theories.

Discussion on the implications of noncommutative spacetime for causality.

Abstract

In this brief report, the microcausility of quantum field theory on spin-induced noncom- mutative spacetime is discussed. It is found that for spacelike seperation the microcausality is not obeyed by the theory generally. It means that Lorentz covariance can not guaran- tee microcausality in quantum field thoery. We also give some comments about quantum field thoeries on such noncommutative spacetime and the relations between noncommutative spacetime and causality.