Renormalization of quantum field theory on curved space-times: a causal approach.
type: Dataset
description: The subject of the thesis is the construction of a perturbative quantum theory of interacting fields on a curved space-time, following a point of view pioneered by Stueckelberg and Bogoliubov and developed by Epstein-Glaser on the flat Minkowski space-time. In 2000, a breakthrough was done by Brunetti and Fredenhagen who were able to extend the Epstein-Glaser theory by exploiting the point of view developed by Radzikowski to define quantum states on a curved space-time in terms of wave-front sets. These results were further extended by Fredenhagen, Brunetti, Hollands, Wald, Rejzner, etc. to Yang-Mills fields and the gravitation. However, even for theories without gauge invariance, many mathematical details were left unexplored and unquestioned. Our task was precisely to derive fully rigorously this theory in the case there is no gauge invariance. We propose in our work a complete review of the result, solving numerous questions, adding many new results around this program and, eventually, giving more precise details on the counterterms and ambiguities in the renormalization process, and a deeper understanding of the geometry of the wave front set of the n-point functions.
issued: 2026-05-07T19:32:39.089981
language: en
modified: 2026-05-07T19:32:39.089985
contact point: Organization
  fn: CCSD
keyword: algebres-de-hopf
keyword: analyse-microlocale
keyword: distribution-theory
keyword: geometrie-symplectique
keyword: hopf-algebras
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-famathematics-mathfunctional-analysis-mathfa
keyword: mathmath-mpmathematics-mathmathematical-physics-math-ph
keyword: microlocal-analysis
keyword: physqphyphysics-physicsquantum-physics-quant-ph
keyword: quantum-field-theory-on-curved-space-times
keyword: renormalisation
keyword: renormalization
keyword: symplectic-geometry
keyword: theorie-des-distributions
keyword: theorie-quantique-des-champs
keyword: theses
landing page: https://theses.hal.science/tel-00918759

Renormalization of quantum field theory on curved space-times: a causal approach.
type: Distribution
format: HTML
issued: 2026-05-07T19:32:39.111317
modified: 2026-05-07T19:32:39.072510
access URL: https://theses.hal.science/tel-00918759

test_moissonnage_selune
type: Agent