Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model

TL;DR

This paper examines twisted covariance in noncommutative spacetime models, revealing that the apparent tensor nature of theta is formal and that rejecting certain states to preserve covariance breaks relativity, raising concerns about observable implications.

Contribution

It demonstrates that twisted covariance can be reformulated within the DFR model and shows that rejecting localization states to maintain covariance is unnecessary and breaks relativity.

Findings

Twisted covariance is equivalent to the DFR model when discarding certain states.

Rejecting localization states to preserve covariance is an unnecessary assumption.

The formal tensor nature of theta does not imply physical invariance under Lorentz transformations.

Abstract

We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.