Causality and statistics on the Groenewold-Moyal plane

TL;DR

This paper explores quantum theories on the Groenewold-Moyal plane, highlighting their unique properties like Lorentz and CPT violation, causality issues, and twisted statistics, which could lead to observable experimental effects.

Contribution

It demonstrates how noncommutative spacetime models predict novel phenomena such as forbidden transitions and anisotropies, providing testable experimental signatures.

Findings

Prediction of Pauli forbidden transitions

Anisotropies in cosmic microwave background radiation

Lorentz and CPT violations in scattering amplitudes

Abstract

Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.