, Volume 295, Issue 3, pp 701-729
Date: 11 Feb 2010

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

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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 θ 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 θ is only hidden in the formalism: in particular if θ 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 θ in arbitrarily selected privileged frames.

Communicated by Y. Kawahigashi