title: A Temporal Functional Renormalisation Group Approach to Non-Perturbative Quantum Dynamics
creator: Heller, Markus
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-530
subject: 530 Physics
description: In this work, we substantially advance the formalism of the temporal functional renormalisation group which constitutes a non-perturbative framework for computing the dynamics of correlation functions in quantum field theories. To that end we carefully revisit the derivation of the temporal flow equation, paying particular attention to properties arising from a causal temporal regulator.  We use the manifest causality of the formalism to integrate the general temporal flow analytically. The result are novel one-loop exact equations for fully dressed correlation functions. Further leveraging causality, we derive the complete Dyson-Schwinger hierarchy and the s-channel effective vertex in terms of specific truncations of the temporal flow. We solve the problem of renormalising the general causal temporal flow. We demonstrate that certain types of causal integral equations can be solved by an explicit numerical method. We numerically solve the integrated flow in a truncation involving the propagator of the $\phi^3$-theory in $1+1$ dimensions. Our results indicate the emergence of universal dynamics. Due to the high degree of flexibility of approximation schemes of the temporal flow, energy conservation in generic truncations is not guaranteed automatically but becomes a non-trivial feature instead. We explore energy-conserving truncations by deriving the causal temporal flow of the energy-momentum tensor, which we integrate analytically.
date: 2021
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/30290/7/Dissertation_Heller_Final.pdf
identifier: DOI:10.11588/heidok.00030290
identifier: urn:nbn:de:bsz:16-heidok-302901
identifier:   Heller, Markus  (2021) A Temporal Functional Renormalisation Group Approach to Non-Perturbative Quantum Dynamics.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/30290/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng