<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Topological data analysis and geometry in quantum field dynamics"^^ . "Many non-perturbative phenomena in quantum field theories are driven or accompanied by non-local excitations, whose dynamical effects can be intricate but difficult to study. Amongst others, this includes diverse phases of matter, anomalous chiral behavior, and non-equilibrium phenomena such as non-thermal fixed points and thermalization. Topological data analysis can provide non-local order parameters sensitive to numerous such collective effects, giving access to the topology of a hierarchy of complexes constructed from given data.\r\n\t\r\nThis dissertation contributes to the study of topological data analysis and geometry in quantum field dynamics. A first part is devoted to far-from-equilibrium time evolutions and the thermalization of quantum many-body systems. We discuss the observation of dynamical condensation and thermalization of an easy-plane ferromagnet in a spinor Bose gas, which goes along with the build-up of long-range order and superfluidity. In real-time simulations of an over-occupied gluonic plasma we show that observables based on persistent homology provide versatile probes for universal dynamics off equilibrium. Related mathematical effects such as a packing relation between the occurring persistent homology scaling exponents are proven in a probabilistic setting.\r\n\t\r\nIn a second part, non-Abelian features of gauge theories are studied via topological data analysis and geometry. The structure of confining and deconfining phases in non-Abelian lattice gauge theory is investigated using persistent homology, which allows for a comprehensive picture of confinement. More fundamentally, four-dimensional space-time geometries are considered within real projective geometry, to which canonical quantum field theory constructions can be extended. This leads to a derivation of much of the particle content of the Standard Model.\r\n\t\r\nThe works discussed in this dissertation provide a step towards a geometric understanding of non-perturbative phenomena in quantum field theories, and showcase the promising versatility of topological data analysis for statistical and quantum physics studies."^^ . "2023" . . . . . . . "Daniel"^^ . "Spitz"^^ . "Daniel Spitz"^^ . . . . . . "Topological data analysis and geometry in quantum field dynamics (PDF)"^^ . . . "Dissertation_Daniel_Spitz.pdf"^^ . . . "Topological data analysis and geometry in quantum field dynamics (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Topological data analysis and geometry in quantum field dynamics (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Topological data analysis and geometry in quantum field dynamics (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Topological data analysis and geometry in quantum field dynamics (Other)"^^ . . . . . . "small.jpg"^^ . . . "Topological data analysis and geometry in quantum field dynamics (Other)"^^ . . . . . . "indexcodes.txt"^^ . . "HTML Summary of #33609 \n\nTopological data analysis and geometry in quantum field dynamics\n\n" . "text/html" . . . "500 Naturwissenschaften und Mathematik"@de . "500 Natural sciences and mathematics"@en . . . "530 Physik"@de . "530 Physics"@en . .