Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros

TL;DR

This paper demonstrates that quantum field theories on Wick-Voros and Moyal noncommutative spacetimes are fundamentally inequivalent, with significant physical differences, highlighting the Moyal plane's unique suitability for such theories.

Contribution

It shows the inequivalence of quantum field theories on Wick-Voros and Moyal planes, revealing the limitations of Wick-Voros in constructing consistent quantum field theories.

Findings

Quantum field theories on Wick-Voros and Moyal planes are inequivalent.

Wick-Voros plane cannot support a fully consistent quantum field theory.

Moyal twist possesses unique features making it preferable for noncommutative QFTs.

Abstract

In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.