Noncommutative version of Borcherds' approach to quantum field theory

Brouder, Christian; Dang, Nguyen Viet; Frabetti, Alessandra

Document type :

Communication dans un congrès avec actes

Title :

Noncommutative version of Borcherds' approach to quantum field theory

Author(s) :

Brouder, Christian [Auteur correspondant]
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]

Conference title :

Frontiers of Fundamental Physics 14

City :

Marseille

Country :

France

Start date of the conference :

2014-07-15

English keyword(s) :

quantization
Hopf algebra
quantum field theory

HAL domain(s) :

Physique [physics]/Physique mathématique [math-ph]

English abstract : [en]

Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this ...
Show more >Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' 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 contains all the terms of the perturbative expansion and we quantize it to recover the expectation values of standard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This construction enables to the second quantize any theory described by a cocommutative Hopf algebra bundle.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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