Gherardo Piacitelli

Twisted Lorentz Covariance as a Disguise


In recent years, a Hopf-theoretical deformation of covariance received much attention as a method of circumventing the fundamental breakdown of covariance of commutation relations among spacetime coordinates, where the commutators are multiples of the identity forming a tensor "constant in all frames". We show that this is perfectly equivalent to let the commutators transform as an ordinary tensor under ordinary Lorentz covariance. Hence the resulting theory is form-covariant, although the relativity of observers remains broken. We understand this in the framework of the fully covariant DFR model of quantum spacetime, as the result of a non invariant selection cryterion of otherwise admissible localisation states.