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Noncommutative version of Borcherds' approach to quantum field theory

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  • معلومة اضافية
    • Contributors:
      Institut de minéralogie, de physique des matériaux et de cosmochimie (IMPMC); Muséum national d'Histoire naturelle (MNHN)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de recherche pour le développement IRD : UR206-Centre National de la Recherche Scientifique (CNRS); Laboratoire Paul Painlevé - UMR 8524 (LPP); Université de Lille-Centre National de la Recherche Scientifique (CNRS); Probabilités, statistique, physique mathématique (PSPM); Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)
    • بيانات النشر:
      HAL CCSD
    • الموضوع:
      2014
    • Collection:
      Université de Lyon: HAL
    • الموضوع:
      Marseille; France
    • نبذة مختصرة :
      International audience ; 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.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/1502.00147; hal-01111764; https://hal.science/hal-01111764; https://hal.science/hal-01111764/document; https://hal.science/hal-01111764/file/ffpbib.pdf; ARXIV: 1502.00147
    • الدخول الالكتروني :
      https://hal.science/hal-01111764
      https://hal.science/hal-01111764/document
      https://hal.science/hal-01111764/file/ffpbib.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.68C2778