Abstract
Perturbative algebraic quantum field theory is a formalism which allows to put perturbative QFT on a solid mathematical basis and solves many conceptual problems. It has proven to be a very successful framework for QFT on curved spacetimes, since it allows to separate the algebraic structure of the theory from the construction of a state. The main idea, inspired by the HaagKastler axiomatic framework, is to define a model of a QFT by giving a net of unital *-algebras, assigned to regions of spacetime. To construct such a model, one starts with a free classical theory, then obtains the free quantum theory via deformation quantization and finally introduces the interaction by means of Epstein-Glaser renormalization. In this overview talk I will show how this method works for the example of the scalar field and how this is related to Schwinger-Dyson equations.
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