Quantum Space-Time and Noncommutative Gauge Field Theories

TL;DR

This thesis explores fundamental aspects and model building in noncommutative quantum field theory, addressing Lorentz invariance issues and constructing a noncommutative version of the MSSM.

Contribution

It investigates methods to eliminate Lorentz violation in noncommutative theories and develops a noncommutative Minimal Supersymmetric Standard Model.

Findings

Elimination of Lorentz violating effects via parameter integration

Analysis of gauge symmetry restrictions in noncommutative models

Construction of a noncommutative MSSM

Abstract

The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.