On general properties of Lorentz invariant formulation of noncommutative quantum field theory

TL;DR

This paper investigates Lorentz invariant noncommutative quantum field theories, revealing issues with causality and inequivalence of perturbation approaches, highlighting fundamental differences from canonical noncommutative theories.

Contribution

It demonstrates that Lorentz invariant noncommutative QFTs lack causality and that their Hamiltonian and covariant perturbation theories remain inequivalent, unlike canonical models.

Findings

Causality does not hold in Lorentz invariant noncommutative QFTs.

Hamiltonian and covariant perturbation theories are inequivalent.

Infinite nonlocality affects spacetime causality in these theories.

Abstract

We study general properties of certain Lorentz invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge causality condition. This is the consequence of the infinite nonlocality of the theory getting spread in all spacetime directions. We also show that the time-ordered perturbation theory arising from the Hamiltonian formulation of noncommutative quantum field theories remains inequivalent to the covariant perturbation theory with usual Feynman rules even after restoration of Lorentz symmetry.