# The Groenewold - Moyal Plane and its Quantum Physics

## TL;DR

This paper reviews quantum physics on the Groenewold-Moyal plane, highlighting its unique features like causality violation, Lorentz and CPT non-invariance, and twisted statistics, which lead to testable experimental predictions.

## Contribution

It provides a comprehensive survey of the properties and potential experimental implications of quantum theories formulated on the GM plane.

## Key findings

- Prediction of Pauli-forbidden transitions
- Anisotropies in cosmic microwave background
- Lorentz and CPT violations in scattering

## Abstract

Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal(GM) plane exhibit many interesting properties such as causality violation, Lorentz and CPT non-invariance and twisted statistics. Such violations lead to many striking features that may be tested experimentally. Thus these theories predict Pauli-forbidden transitions due to twisted statistics, anisotropies and acausal effects in the cosmic microwave background radiation in correlations of observables and Lorentz and CPT violations in scattering amplitudes. Such features of quantum physics on the GM plane are surveyed in this review.