Field Theories and Vortices with Nontrivial Geometry

This thesis investigates aspects of field theories and soliton solutions with nontrivial topology. In particular we explore the following effective models: a limited sector of the scalar Electroweak theory called extended Abelian Higgs model, and a classical mechanics model derived from the low energy SU(2) Yang-Mills theory.The extended Abelian Higgs model applied on two-component plasma of charged particles is studied numerically. We find evidence that the model admits straight twisted line vortices. The result is described by an energy function that acquires a minimum value for a non-trivial twist. In addition to the twisted line vortices the result also suggests that stable torus shaped solitons are solutions of the theory…


1 Introduction
2 Foundations
2.1 Symmetry Principle
2.2 Gauge Field Theory
2.3 Broken Symmetry and Solitons
3 Topological Aspects
3.1 Solitons
3.2 Models
3.3 Knots
3.4 Generalised Skyrme System
4 Spontaneously Broken Theories
4.1 The GWS Model
4.2 Abelian Higgs Model
4.3 Nielsen-Olesen Vortices
4.4 Extended Abelian Higgs Model
5 Electromagnetic Plasma
5.1 Virial Theorem
5.2 Effective Model
6 Effective Theories
6.1 General Background
6.2 Algebraic Method
7 Yang Mills Vacuum
7.1 YM Theory in Dual Decomposition
7.2 One-Loop Effective Yang-Mills Theory
7.3 Classical Mechanics Model of the YM Theory
8 Epilogue
9 Summary of the Included Papers
9.1 Paper

Author: Torokoff, Kristel

Source: Uppsala University Library

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