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Osterwalder-Schrader Reconstruction and the Free Field

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Title: Osterwalder-Schrader Reconstruction and the Free Field
Author(s): Hatakka, Ilari
Contributor: University of Helsinki, Faculty of Science
Degree program: Master 's Programme in Theoretical and Computational Methods
Specialisation: no specialization
Language: English
Acceptance year: 2023
In quantum field theory the objects of interest are the n-point vacuum expectations which can be calculated from the path integral. The path integral usually used in physics is not well-defined and the main motivation for this thesis is to give axioms that a well-defined path integral candidate has to at least satisfy for it to be physically relevant - we want the path integral to have properties which allow us to reconstruct the physically interesting objects from it. The axioms given in this thesis are called the Osterwalder-Schrader axioms and the reconstruction of the physical objects from the path integral satisfying the axioms is called the Osterwalder-Schrader reconstruction. The Osterwalder-Schrader axioms are special in the sense that they are stated in terms of the Euclidean spacetime instead of the physically relevant Minkowski spacetime. As the physical objects live in Minkowski spacetime this means that when reconstructing the physically relevant objects we have to go back to Minkowski spacetime at some point. This thesis has three parts (and an introduction). In the first part we give a brief introduction to parts of functional analysis which we will need later - theory about distributions and about generators of families of operators. The second part is about the Osterwalder-Schrader axioms and about the reconstruction of the physically relevant objects from the path integral. In the last part we check that the path integral for the free field of mass m satisfies the Osterwalder-Schrader axioms.
Keyword(s): QFT Constructive quantum field theory

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