Construction of minimal gauge invariant subsets of Feynman diagrams with loops in gauge theories.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2005)
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|Item Type:||Ph.D. Thesis|
|Title:||Construction of minimal gauge invariant subsets of Feynman diagrams with loops in gauge theories|
In this work, we consider Feynman diagrams with loops in renormalizable gauge theories with and without spontaneous symmetry breaking. We demonstrate that the set of Feynman diagrams with a fixed number of loops, contributing to the expansion of a connected Green's function in a fixed order of perturbation theory, can be partitioned into minimal gauge invariant subsets by means of a set of graphical manipulations of Feynman diagrams, called gauge flips. To this end, we decompose the Slavnov-Taylor identities for the expansion of the Green's function in such a way that these identities can be defined for subsets of the set of all Feynman diagrams. We then prove, using diagrammatical methods, that the subsets constructed by means of gauge flips really constitute minimal gauge invariant subsets. Thereafter, we employ gauge flips in a classification of the minimal gauge invariant subsets of Feynman diagrams with loops in the Standard Model. We discuss in detail an explicit example, comparing it to the results of a computer program which has been developed in the context of the present work.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||Eichinvariante Untermengen, Feynmandiagramme mit Schleifen|
|Divisions:||05 Department of Physics|
|Date Deposited:||17 Oct 2008 09:22|
|Last Modified:||07 Dec 2012 11:51|
|Referees:||Manakos, Prof. Dr. Panagiotis and Wambach, Prof. Dr. Jochen|
|Advisors:||Manakos, Prof. Dr. Panagiotis|
|Refereed:||6 June 2005|