Séminaire Physique mathématique ICJ

A. Schenkel, "Homotopical algebraic quantum field theory"

Fokko du Cloux (Institut Camille Jordan)

Fokko du Cloux

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne
An algebraic quantum field theory is an assignment of algebras to spacetimes. These algebras should be interpreted as quantizations of the algebras of functions on the moduli spaces of a classical field theory. In many cases of interest, especially in gauge theories, these moduli spaces are not conventional spaces but `higher spaces' called stacks. Consequently, functions on such spaces do not form an algebra but a `higher algebra' which one may describe by homotopical algebra. This motivates us to study assignments of `higher algebras' to spacetimes, which is what I call homotopical algebraic quantum field theory. In this talk I will clarify the above picture and explain its advantages compared to traditional algebraic quantum field theory. For this I will also present simple toy-models related to Abelian gauge theory and homotopy Kan extensions.
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