caa a22 4500 44538624X CHVBK 20180317143033.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10714-011-1263-x doi (NATIONALLICENCE)springer-10.1007/s10714-011-1263-x Quantum geons and noncommutative spacetimes [Elektronische Daten] [A. Balachandran, A. Ibort, G. Marmo, M. Martone] Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincaré group algebra acts on it with a Drinfel'd-twisted coproduct, however the latter is not appropriate for more complicated spacetimes such as those containing Friedman-Sorkin (topological) geons. They have rich diffeomorphisms and mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group S N . We generalise the Drinfel'd twist to (essentially all) generic groups including finite and discrete ones, and use it to deform the commutative spacetime algebras of geons to noncommutative algebras. The latter support twisted actions of diffeomorphisms of geon spacetimes and their associated twisted statistics. The notion of covariant quantum fields for geons is formulated and their twisted versions are constructed from their untwisted counterparts. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli's principle, seem to be one of the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out. Springer Science+Business Media, LLC, 2011 Quantum field theory nationallicence Noncommutative spacetime nationallicence Quantum Geons nationallicence Balachandran A. Department of Physics, Syracuse University, 13244-1130, Syracuse, NY, USA aut Ibort A. Departamento de Matemáticas, Universitá Carlos III de Madrid, 28911, Leganés, Madrid, Spain aut Marmo G. Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia, 80126, Napoli, Italy aut Martone M. Department of Physics, Syracuse University, 13244-1130, Syracuse, NY, USA aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/12(2011-12-01), 3531-3567 0001-7701 43:12<3531 2011 43 10714 https://doi.org/10.1007/s10714-011-1263-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-011-1263-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balachandran A. Department of Physics, Syracuse University, 13244-1130, Syracuse, NY, USA aut NATIONALLICENCE 700 1- Ibort A. Departamento de Matemáticas, Universitá Carlos III de Madrid, 28911, Leganés, Madrid, Spain aut NATIONALLICENCE 700 1- Marmo G. Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia, 80126, Napoli, Italy aut NATIONALLICENCE 700 1- Martone M. Department of Physics, Syracuse University, 13244-1130, Syracuse, NY, USA aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/12(2011-12-01), 3531-3567 0001-7701 43:12<3531 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer