Ondreka, David (2005):
Construction of minimal gauge invariant subsets of Feynman diagrams with loops in gauge theories.
Darmstadt, Technische Universität, TU Darmstadt,
[Ph.D. Thesis]
Abstract
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.
| Item Type: |
Ph.D. Thesis
|
| Erschienen: |
2005 |
| Creators: |
Ondreka, David |
| Title: |
Construction of minimal gauge invariant subsets of Feynman diagrams with loops in gauge theories |
| Language: |
English |
| Abstract: |
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 |
| Publisher: |
Technische Universität |
| Uncontrolled Keywords: |
Eichinvariante Untermengen, Feynmandiagramme mit Schleifen |
| Divisions: |
05 Department of Physics |
| Date Deposited: |
17 Oct 2008 09:22 |
| URL / URN: |
urn:nbn:de:tuda-tuprints-5695 |
| License: |
only the rights of use according to UrhG |
| PPN: |
|
| Referees: |
Manakos, Prof. Dr. Panagiotis ; Wambach, Prof. Dr. Jochen |
| Refereed / Verteidigung / mdl. Prüfung: |
6 June 2005 |
| Alternative keywords: |
| Alternative keywords | Language |
|---|
| gauge invariant subsets, feynman diagrams with loops | English |
|
| Alternative Abstract: |
| Alternative abstract | Language |
|---|
Diese Arbeit beschäftigt sich mit Feynmandiagrammen mit Schleifen in renormierbaren Eichtheorien mit oder ohne spontane Symmetriebrechung. Es wird gezeigt, dass die Menge der Feynmandiagramme, die zur Entwicklung einer zusammenhängenden Green'schen Funktion in einer bestimmten Schleifenordnung beitragen, mit Hilfe von graphischen Manipulationen an Feynmandiagrammen, sogenannten Eichflipps, in minimal eichinvariante Untermengen zerlegt werden kann. Zu diesem Zweck werden die Slavnov-Taylor-Identitäten für die Entwicklung der Green'schen Funktionen in Schleifenordnung so zerlegt, dass sie für Untermengen der Menge aller Feynmandiagramme definiert werden können. Es wird dann mit diagrammatischen Methoden bewiesen, dass die mittels Eichflipps konstruierten Untermengen tatsächlich minimal eichinvariante Untermengen sind. Anschließend werden die Eichflipps benutzt, um die minimal eichinvarianten Untermengen von Feynmandiagrammen mit Schleifen im Standardmodell zu klassifizieren. Es wird ein ausführliches Beispiel diskutiert und mit Resultaten verglichen, die mit Hilfe eines für die vorliegende Arbeit entwickelten Computerprogramms erhalten wurden. | German |
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