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Quantum field theory via vertex algebras

Olbermann, Heiner 2010. Quantum field theory via vertex algebras. PhD Thesis, Cardiff University.

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We investigate an alternative formulation of quantum field theory that elevates the Wilson- Zimmermann operator product expansion (OPE) to an axiom of the theory. We observe that the information contained in the OPE coefficients may be straightforwardly repackaged into "vertex operators". This way of formulating quantum field theory has quite obvious similarities to the theory of vertex algebras. As examples of this framework, we discuss the free massless boson in D dimensions and the massless Thirring model. We set up perturbation theory for vertex algebras. We discuss a general theory of perturbations of vertex algebras, which is similar to the Hochschild cohomology describing the deformation theory of ordinary algebras. We pass on to a more explicit discussion by looking at perturbations of the free massless boson in D dimensions. The perturbations we consider correspond to some interaction Lagrangian P(<p) = A Cp if. We construct the perturbations by exploiting the associativity of the vertex operators and the field equation in perturbative form. We develop a set of graphical rules that display the vertex operators as certain multiple series reminiscent of the hypergeometric series.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
ISBN: 9781303218330
Date of First Compliant Deposit: 30 March 2016
Last Modified: 19 Mar 2016 23:31

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