Noncommutative Field Theory and Lorentz Violation

TL;DR

This paper explores how noncommutative field theories inherently involve Lorentz violation, linking them to standard-model extensions and discussing experimental bounds on noncommutativity scale.

Contribution

It demonstrates the equivalence between noncommutative theories and Lorentz-violating standard-model extensions, providing theoretical insights and experimental constraints.

Findings

Noncommutative theories are equivalent to Lorentz-violating standard-model extensions.

Experimental data constrains the noncommutativity scale to about (10 TeV)^{-2}.

Theoretical implications of Lorentz violation in noncommutative field theories are discussed.

Abstract

The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV)^{-2}.