title: Topological data analysis and geometry in quantum field dynamics
creator: Spitz, Daniel
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-530
subject: 530 Physics
description: 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.  	  This 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.  	  In 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.  	  The 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.
date: 2023
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/33609/1/Dissertation_Daniel_Spitz.pdf
identifier: DOI:10.11588/heidok.00033609
identifier: urn:nbn:de:bsz:16-heidok-336098
identifier:   Spitz, Daniel  (2023) Topological data analysis and geometry in quantum field dynamics.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/33609/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng