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Noncommutative geometry, gauge theory and renormalization

Abstract : Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of a noncommutative scalar model a harmonic term, which renders it renormalizable. One aim of this thesis is the extension of this procedure to gauge theories on the Moyal space. Indeed, we have introduced a new noncommutative gauge theory, strongly related to the Grosse-Wulkenhaar model, and candidate to renormalizability. We have then studied the most important properties of this action, and in particular its vacuum configurations. Finally, we give a mathematical interpretation of this new action in terms of a derivation-based differential calculus associated to a superalgebra. This work contains among the results of this PhD, an introduction to noncommutative geometry, an introduction to epsilon-graded algebras, defined in this thesis, and an introduction to renormalization of scalar (wilsonian and BPHZ point of view) and gauge quantum field theories.
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Contributor : Axel de Goursac <>
Submitted on : Thursday, July 8, 2010 - 2:03:29 PM
Last modification on : Wednesday, September 16, 2020 - 4:04:55 PM
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  • HAL Id : tel-00498767, version 1



Axel de Goursac. Noncommutative geometry, gauge theory and renormalization. Mathematics [math]. Université Paris Sud - Paris XI, 2009. English. ⟨tel-00498767⟩



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