Construction of operator product expansion coefficients via consistency conditions

TL;DR

This thesis develops an iterative scheme based on Hollands' axiomatic approach to construct operator product expansion coefficients in quantum field theory, demonstrated through a perturbative analysis of 3D Euclidean -theory.

Contribution

It introduces a novel iterative algorithm for calculating OPE coefficients within Hollands' framework, applied to a toy model in perturbative quantum field theory.

Findings

Constructed OPE coefficients up to second order in the toy model

Identified general features of OPE coefficients at arbitrary order

Compared new method with traditional computation approaches

Abstract

In this thesis an iterative scheme for the construction of operator product expansion (OPE) coefficients is applied to determine low order coefficients in perturbation theory for a specific toy model. We use the approach to quantum field theory proposed by S. Hollands [arXiv:0802.2198], which is centered around the OPE and a number of axioms on the corresponding OPE coefficients. This framework is reviewed in the first part of the thesis. In the second part we apply an algorithm for the perturbative construction of OPE coefficients to a toy model: Euclidean $\varphi^6$-theory in 3-dimensions. Using a recently found formulation in terms of vertex operators and a diagrammatic notation in terms of trees [arXiv:0906.5313v1], coefficients up to second order are constructed, some general features of coefficients at arbitrary order are presented and an exemplary comparison to the corresponding customary method of computation is given.