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Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics
[Thesis]. Manchester, UK: The University of Manchester; 2012.
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Abstract
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.
Layman's Abstract
Our everyday experience of the world is of something macroscopic, i.e., somethingcontaining large objects that we can touch. Intellectually, we can appreciate thatthese objects are made up of microscopic pieces like atoms and molecules, but thisremains something intangible to our human senses. For instance, we know that theair around us is a gas of molecules. Nevertheless, when deciding whether to put ona jumper, we don’t ask ourselves what each of these molecules is doing. Instead, wesimply ask ourselves how warm it is. The temperature of the air as a whole is whatmatters to us, not the properties of the billions of individual air molecules. Yet,these things must be connected; the temperature must somehow be a consequenceof the individual behaviour of these billions of molecules.However, there are also macroscopic objects that are beyond our everyday ex-perience; objects that are unimaginably hot and dense and contain incomprehensibleamounts of energy. One example is the infant Universe shortly after the Big Bang.We want to understand the properties of this, the largest object that we know of,in terms of the behaviour of the very smallest objects. These are the elementaryparticles, the building blocks out of which everything is made. The connection be-tween the microscopic properties of these individual elementary particles and themacroscopic properties of such massive collections of these particles is the subjectof this thesis.