In this thesis, we develop a perturbative formulation of non-equilibrium thermal quantum field theory, capable of describing the evolution of both temporal and spatial inhomogeneities in relativistic, quantum-statistical ensembles. We begin with a review of the necessary prerequisites from classical thermodynamics, classical and quantum statistical mechanics, quantum field theory and equilibrium thermal field theory. Setting general boundary conditions on the ensemble expectation values of products of interaction-picture creation and annihilation operators, we derive free propagators in which space-time translational invariance is explicitly broken. By means of the Schwinger-Kelydsh, closed-time path formalism, we are then able to introduce a path-integral description that accounts consistently for these temporal and spatial inhomogeneities. Subsequently, we develop a time-dependent perturbation theory that is free of the pathologies previously thought to spoil such approaches to non-equilibrium dynamics. Following an unambiguous definition of the number density of particles, we derive from first principles perturbative, field-theoretic evolution equations for statistical distribution functions. These evolution equations do not rely on the gradient expansion of so-called Wigner functions, as is necessary in the alternative Kadanoff-Baym approach, and are consistent with the well-known Boltzmann equations in the classical limit. Finally, with reference to a simple toy model, we highlight the appearance of processes otherwise kinematically disallowed in existing approaches to thermal field theory. These evanescent contributions are a consequence of the microscopic violation of energy conservation and are shown to be significant to the early-time evolution of non-equilibrium systems. We observe that the spectral evolution oscillates with time-dependent frequencies, which is interpreted as a signal of non-Markovian, memory effects.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:564344 |
| Date | January 2012 |
| Creators | Millington, Peter William |
| Contributors | Pilaftsis, Apostolos |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/thermal-quantum-field-theory-and-perturbative-nonequilibrium-dynamics(9e2e162f-124c-4f97-9c01-9f585d7aedb4).html |
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