On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT

TL;DR

This paper shows that noncommutative space-time with constant commutation relations can be interpreted in a Lorentz-invariant manner using twisted Poincaré symmetry, supporting previous approaches in noncommutative quantum field theory.

Contribution

It introduces a Lorentz-invariant interpretation of noncommutative space-time via twisted Poincaré symmetry, clarifying its implications for noncommutative quantum field theory.

Findings

Noncommutative space-time can be Lorentz-invariant with twisted symmetry.

Supports previous NC QFT treatments using Lorentz-invariant quantities.

Provides a symmetry-based justification for existing NC QFT approaches.

Abstract

By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_\mu,x_\nu]=i\theta_{\mu\nu}$, where $\theta_{\mu\nu}$ is a {\it constant} real antisymmetric matrix, can be interpreted in a Lorentz-invariant way. The implications of the twisted Poincar\'e symmetry on QFT on such a space-time is briefly discussed. The presence of the twisted symmetry gives justification to all the previous treatments within NC QFT using Lorentz invariant quantities and the representations of the usual Poincar\'e symmetry.