Lorentz covariant field theory on noncommutative spacetime based on DFR algebra

TL;DR

This paper demonstrates that Lorentz covariant field theories can be constructed on noncommutative spacetime when the noncommutativity arises from the DFR algebra, ensuring consistent relativistic descriptions.

Contribution

It introduces a Lorentz covariant field theory framework on noncommutative spacetime based on the DFR algebra, preserving Lorentz symmetry.

Findings

Field theory on noncommutative spacetime can be Lorentz covariant

Lorentz covariance is maintained when noncommutativity is derived from DFR algebra

Provides a consistent approach to relativistic field theories on noncommutative spacetime

Abstract

Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this letter, it is shown that the field theory on noncommutative spacetime is Lorentz covariant if the noncommutativity emerges from the algebra of spacetime operators described by Doplicher, Fredenhagen and Roberts.