## Arts & Sciences Electronic Theses and Dissertations

#### Title

Quantum Fields in Extreme Backgrounds

Spring 5-15-2018

#### Author's School

Graduate School of Arts and Sciences

Physics

#### Degree Name

Doctor of Philosophy (PhD)

Dissertation

#### Abstract

Quantum field theories behave in interesting and nontrivial ways in the presence of intense electric and/or magnetic fields. Describing such behavior correctly, particularly at finite (nonzero) temperature and density, is of importance for particle physics, nuclear physics, astrophysics, condensed matter physics, and cosmology. Incorporating these conditions as external parameters also provides useful probes into the nonperturbative structure of gauge theories.

In this work, formalism for describing matter in a variety of extreme conditions is developed and implemented. We develop several expansions of one-loop finite temperature effects for spinor particles in the presence of magnetic fields, including the effects of confinement, encoded in a nontrivial Polyakov loop. The worldline instanton formalism is extended to the case of finite temperature, which yields a long-sought thermal extension to the celebrated formula of Schwinger for pair production in a constant electric field. The technique is further extended to include the effects of finite density and confinement, as well as some restricted classes of nonabelian electric fields.

A persistent source of difficulty in the study of gauge theories at finite density, and/or in the presence of external electric fields, is the so-called sign problem. We advance a novel duality-based approach for lattice simulation of scalar field theories with complex actions, which yields new insights on the old problem of spatial modulations arising in systems with competing interactions. The approach shows promise for simulating scalar theories at finite density and in the presence of external electric fields, and is capable of handling systems in the universality class of the $i\phi^3$ theory, which determines the critical indices of the Lee-Yang edge transition.

English (en)

#### Chair and Committee

Michael C. Ogilvie

#### Committee Members

Mark G. Alford, P. S. Bhupal Dev, Willem H. Dickhoff, Renato Feres,