Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics

Student thesis: Phd


In this thesis, we develop a perturbative formulation of non-equilibrium thermalquantum field theory, capable of describing the evolution of both temporal and spa-tial inhomogeneities in relativistic, quantum-statistical ensembles. We begin with areview of the necessary prerequisites from classical thermodynamics, classical andquantum statistical mechanics, quantum field theory and equilibrium thermal fieldtheory. Setting general boundary conditions on the ensemble expectation values ofproducts of interaction-picture creation and annihilation operators, we derive freepropagators in which space-time translational invariance is explicitly broken. Bymeans of the Schwinger-Kelydsh, closed-time path formalism, we are then able tointroduce a path-integral description that accounts consistently for these temporaland spatial inhomogeneities. Subsequently, we develop a time-dependent perturba-tion theory that is free of the pathologies previously thought to spoil such approachesto non-equilibrium dynamics.Following an unambiguous definition of the number density of particles, wederive from first principles perturbative, field-theoretic evolution equations for sta-tistical distribution functions. These evolution equations do not rely on the gradientexpansion of so-called Wigner functions, as is necessary in the alternative Kadanoff-Baym approach, and are consistent with the well-known Boltzmann equations inthe classical limit. Finally, with reference to a simple toy model, we highlight theappearance of processes otherwise kinematically disallowed in existing approachesto thermal field theory. These evanescent contributions are a consequence of themicroscopic violation of energy conservation and are shown to be significant to theearly-time evolution of non-equilibrium systems. We observe that the spectral evo-lution oscillates with time-dependent frequencies, which is interpreted as a signal ofnon-Markovian, memory effects.
Date of Award31 Dec 2012
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorApostolos Pilaftsis (Supervisor)


  • non-equilibrium thermal quantum field theory

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