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We compute the electrical conductivity and shear viscosity at leading order in hot Quantum Electrodynamics. Starting from the Kubo relation for electrical conductivity and shear viscosity, we use diagrammatic methods to write down the appropriate integral equations for bosonic and fermionic effective vertices. We also show how Ward identities can be used to put constraints on these integral equations. One of our main results is an equation relating the kernels of the integral equations with functional derivatives of the full self-energy; it is similar to what is obtained with two-particle-irreducible effective action methods. However, since we use Ward identities as our starting point, gauge invariance is preserved. Using these constraints obtained from Ward identities and also power counting arguments, we select the necessary diagrams that must be resummed at leading order. This includes all non-collinear (corresponding to 2 to 2 scatterings) and collinear (corresponding to 1+N to 2+N collinear scatterings) rungs responsible for the Landau-Pomeranchuk-Migdal effect. We also show the equivalence between our integral equations and the linearized Boltzmann equations of Arnold, Moore and Yaffe obtained using effective kinetic theory.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 153-159).

The Casimir effect refers to the primarily attractive force between material bodies due to quantum fluctuations in the electromagnetic field. The Casimir effect is difficult to calculate in general, since it is sensitive to the exact shapes of the bodies and involves contributions from all frequencies. As a result, calculating the Casimir effect between general bodies usually requires a numerical approach. The worldline method computes Casimir energies by creating an ensemble of space-time paths corresponding to a virtual particle interacting with the bodies. This method was originally developed for a scalar fields coupled to an idealized background potential, rather than the vector electromagnetic field interacting with media. This thesis presents work on extending the worldline method to account for the material properties of the interacting bodies, and the polarizations of electromagnetism. This thesis starts by covering background material on path integrals, and quantizing the electromagnetic field in media. The electromagnetic field is decomposed in terms of two scalar fields for planar bodies, where these scalar fields correspond to the transverse-electric and transverse-magnetic polarizations of the electromagnetic field. The worldline path integrals are developed for both polarizations, and solved analytically. Next, numerical methods are developed and tested in the context of planar bodies. The starting positions, and scale of the paths, and shape of the paths are sampled via Monte Carlo methods. The transverse-magnetic path integral also requires specialized methods for estimating derivatives, and path construction. The analytical and numerical results for both worldline path integrals are in agreement with known solutions. Finally, specialized methods are developed for computing derivatives of the worldline Casimir-energy path integrals, allowing for efficient numerical computations of Casimir forces and torques.

Nesta tese estudamos algumas propriedades da eletrodinamica em 2+1 dimensoes. Perturbativamente, esta teoria e inconsistente, devido a ocorrencia de fortes divergencias infravermelhas. E mostrado que tal problemas pode ser sanado quando efeitos nao perturbativos de polarizacao do vacuo sao incorporados, promovendo a melhoria do comportamento infravermelho da teoria. Isto e decorrente da geracao de um termo de chern-simons. Analisamos, tambem, a existencia de estados ligados fermion-fermion, a qual pode ser relevante no contexto da supercondutividade a altas temperaturas. Alem disso, obtemos a contribuicao para o momento magnetico anomalo do fermio vinda da correcao de vertice. Uma motivacao para este trabalho advem de estudos feitos originalmente para o modelo de thirring em 2+1 dimensoes, os quais sao apresentados na parte inicial desta tese. / In this thesis we study some properties of electrodynamics in 2+ 1 dimensions. Perturbatively, inconsistencies appear, due to strong infrared divergencies. It is shown that this problem can be overcome when vacuum polarization effects are nonperturbatively incorporated, leading to a better infrared behavior of the theory. This is a consequence of the generation of a Chern-Simons term. Also, we analyse the existence of fermion-fermion bound states, which may be relevant for high-Tc superconductivity. Furthermore, from the vertex corrections we determine the contribution for the fermion anomalous magnetic moment. A motivation for this work comes from earlier studies in the context of the 2+ 1 dimentional Thirring model. Those studies are presented in the initial part of this thesis.

The dynamical Schwinger effect refers to the creation of electron-positron pairs by a time dependent, spatially homogeneous electric field. It probes the fundamentals of quantum electrodynamics and is sought to be verified with upcoming high-intensity laser installations. In the dynamically assisted Schwinger effect, the pair yield is increased by orders of magnitude through the combination of fields of different field strength and frequency scales. In this thesis we, investigate both processes in the framework of a quantum kinetic equation. We are especially interested in what amplification factors can be achieved by the assisting field and whether intermediately large mode occupation numbers have a physical significance and could serve as a verification of the Schwinger effect. For the latter goal, we couple our system to a quantized radiation field that serves as a secondary (photon) probe and study its spectrum, as the afterglow of the dynamical Schwinger effect. / Als dynamischen Schwingereffekt bezeichnet man die Erzeugung von Elektron-Positron-Paaren durch ein zeitabhängiges, räumlich homogenes elektrisches Feld. Er dient zur Untersuchung der Grundlagen der Quantenelektrodynamik und es wird versucht, ihn an zukünftigen Hochintensitäts-Laseranlagen zu verifizieren. Bei dem dynamisch assistierten Schwingereffekt wird die Paarausbeute durch eine Kombination von Feldern mit unterschiedlichen Feldstärken- und Frequenzskalen um mehrere Größenordnungen erhöht. In dieser Dissertation untersuchen wir beide Prozesse im Rahmen einer quantenkinetischen Gleichung. Wir interessieren uns besonders dafür, welche Verstärkungsfaktoren durch das assistierende Feld erreicht werden können und ob intermediär große Modenbesetzungszahlen physikalische Signifikanz haben und als Verifizierung des Schwingereffekts dienen können. Für zweiteres Ziel koppeln wir unser System an ein quantisiertes Strahlungsfeld, das als sekundäres (Photonen-) Signal dient, und untersuchen dessen Spektrum, das Nachglühen des dynamischen Schwingereffekts.

We use quantum electrodynamics (QED) to investigate the possibility of radiative interference from a single laser-driven electron wave packet. Intuition gleaned from classical electrodynamics suggests that radiation from a large electron wave packet might interfere destructively when different regions of the packet oscillate out of phase with each other. We show that when the incident light is represented with a multi-mode coherent state, the relative phases of the electron's constituent momenta have no influence of the amount of scattered light. Hence, the radiation does not depend on the amount of free-particle spreading experienced by the electron before the interaction. This result is shown to hold to all orders of perturbation theory. We extend our conclusions using the Furry picture of QED, where the (now-classical) incident light pulse is treated non-perturbatively with Volkov functions. We connect our results to a first-quantized picture by comparing transition probabilities between QED and semiclassical models. We are able to match these probabilities by choosing the classical scattered light field to be a single mode with energy hω'.

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