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Abstract
The concept of symmetry is without doubt the most significant centerpiece of modern science. Our current understanding of the visible universe is phrased into a basic set of equations describing what we call 'gauge theories'. The laws governing the dynamics of nature have been derived studying the symmetry properties of these equations, that is their invariance or noninvariance under certain symmetry 'transformations'. Because of their grand success and while seeming omnipotent, it came as a sensational surprise, that nature mysteriously does not obey some of the above symmetry principles by mechanisms that are elusive: Quantum Anomalies. The intriguing feature of the anomalous violation of symmetries is that it cannot be understood by the defining set of equations that were postulated to comprise the physical content of nature, but rather from the structures of quantum theories itself. Quantum anomalies emerge from the transition from the classical to the quantum level of nature, and researchers have realized that the properties of the physical vacuum (that is the quantum equivalent of 'nothing') are very nontrivial.
Symmetries are the cornerstones of gauge theories and the fundamental forces they describe. The vast majority of visible matter is governed by the strong interactions, formulated through the theory of Quantum Chromodynamics (QCD). In this context, symmetry principles also dictate the existence of another mysterious concept: topology. Topology is the principle used to describe the fundamental structure of an object, invariant under a certain transformation. In physics it describes the invariance of the aforementioned basic set of equations under continuous and hence structurepreserving manipulations. It is very suggestive that quantum anomalies and the concept of topology should be intimately related and in fact this assertion is most famously confirmed by the socalled axial anomaly.
The physics of quantum anomalies and topology is intriguing and often mysterious, yet central to many of the fundamental mechanisms of nature. As the anomalous violation of classical symmetries in the earliest stages of the universe is conjectured to be responsible for the dominance of matter over antimatter, researchers attempt to recreate the dynamics of matter under extreme conditions at heavy ion collider experiments and thus understand these challenging mechanisms. In the early universe as well as in present day experiments the emergence of quantum anomalies is tied to \textit{outofequilibrium} systems.
In this thesis we focus on a comprehensive attempt at establishing the theoretical foundations of the nonequilibrium description of anomalous and topological dynamics. To this end we present a selection of different techniques and approximation schemes, which are motivated by the properties of the spacetime evolution of QCD matter in ultrarelativistic heavy ion collisions. Most importantly we aim to illustrate that the techniques, which are presented here, are applicable to a number of systems in nature, starting from strongfield laser physics to cosmology. The nature of topological effects is much richer in outofequilibrium systems and in accord with present progress in the experimental study of anomalous effects, we hope to contribute to the establishment of a novel view on anomalies and topology beyond the previous equilibrium paradigm.
Item Type:  Dissertation 

Supervisor:  Pawlowski, Prof. Dr. Jan Martin 
Date of thesis defense:  21 June 2017 
Date Deposited:  28 Jun 2017 11:35 
Date:  2017 
Faculties / Institutes:  The Faculty of Physics and Astronomy > Dekanat der Fakultät für Physik und Astronomie The Faculty of Physics and Astronomy > Institute for Theoretical Physics 
Subjects:  530 Physics 