Authors: A P Balachandran A Ibort G Marmo M Martone
Publish Date: 2011/03/11
Volume: 2011, Issue: 3, Pages: 57-
Abstract
A spinless quantum covariant field φ on Minkowski spacetime mathcalMd + 1 obeys the relation Ua ΛφxUa Λ−1 = φΛx + a where a Λ is an element of the Poincaré group Open image in new window and U a Λ → Ua Λ is an unitary representation on quantum vector states It expresses the fact that Poincaré transformations are being unitarily implemented It has a classical analogy where field covariance shows that Poincaré transformations are canonically implemented Covariance is selfreproducing products of covariant fields are covariant We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes In this way all our earlier results on dressing statistics etc for Moyal spacetimes are derived transparently For the Voros algebra covariance and the ∗operation are in conflict so that there are no ∗covariant Voros fields a result we found earlier The notion of Drinfel’d twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons For twists involving nonabelian groups the emergent spacetimes are nonassociative
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