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Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: 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 …
Quantum Geons And Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Quantum Geons And Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone
Physics - All Scholarship
Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincare group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group SN. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the …