Noncommutative version of Borcherds’ ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Noncommutative version of Borcherds’ approach toquantum field theory
Author(s) :
Brouder, Christian [Auteur]
Institut de minéralogie, de physique des matériaux et de cosmochimie [IMPMC]
Dang, Nguyen Viet [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Frabetti, Alessandra [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Institut de minéralogie, de physique des matériaux et de cosmochimie [IMPMC]
Dang, Nguyen Viet [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Frabetti, Alessandra [Auteur]
Probabilités, statistique, physique mathématique [PSPM]
Journal title :
PoS - Proceedings of Science
Publisher :
SISSA
Publication date :
2015
ISSN :
1824-8039
HAL domain(s) :
Physique [physics]
English abstract : [en]
Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantumfield theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle overa smooth manifold. However, this ...
Show more >Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantumfield theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle overa smooth manifold. However, this framework looses its geometric meaning when Borcherdsintroduces a (graded) commutative normal product. We present a fully geometric version ofBorcherds’ quantization where the (external) tensor product plays the role of the normal product.We construct a noncommutative many-body Hopf algebra and a module over it which containsall the terms of the perturbative expansion and we quantize it to recover the expectation values ofstandard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This constructionenables to the second quantize any theory described by a cocommutative Hopf algebrabundle.Show less >
Show more >Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantumfield theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle overa smooth manifold. However, this framework looses its geometric meaning when Borcherdsintroduces a (graded) commutative normal product. We present a fully geometric version ofBorcherds’ quantization where the (external) tensor product plays the role of the normal product.We construct a noncommutative many-body Hopf algebra and a module over it which containsall the terms of the perturbative expansion and we quantize it to recover the expectation values ofstandard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This constructionenables to the second quantize any theory described by a cocommutative Hopf algebrabundle.Show less >
Language :
Anglais
Popular science :
Non
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