Applications of Quantum Field Theory to Many Body Systems: From Ultracold Atoms to Gravitational Waves [electronic resource].

9780438970571

Ann Arbor : ProQuest Dissertations & Theses, 2018.

1 online resource (146 p.)

Access is available to the Yale community.

Access restricted by licensing agreement.

We apply techniques of quantum field theory to two many-body systems. namely the study of ultracold atoms and of gravitational waves from compact objects. The first part of the thesis deals with the study of ultracold atomic gases near the unitarity limit. The field theoretical realization of this system is an example of a Non-relativistic Conformal Field Theory (NRCFT). We systematically analyze the structure of the Operator Product Expansion (OPE) for operators with non-zero particle number in an NRCFT. We show that the OPE can be organized into conformal multiplets which contain a primary operator and its descendants. We determine the OPE coefficients of descendant operators in terms of the corresponding primary. We demonstrate that the OPE converges, with the convergence rate being exponential in operator dimensions. This puts the analysis of such theories using the OPE on a firm footing. The second part of the thesis is a study of radiation from a system of many sources in classical field theories. Motivated by the BCJ double copy in quantum field theory. we demonstrate a correspondence between perturbative solutions of classical scalar, gauge and gravity theories at leading order in perturbation. Our first result is that classical Yang-Mills radiation from a system of colored particles can be obtained from classical bi-adjoint scalar radiation emitted by a corresponding system of bi-adjoint colored particles, via a simple set. of color-kinematic substitution rules. This completes a two-fold double copy that can be used to generate classical gravitational radiation emitted by a collection of dynamical point sources. from the simpler bi-adjoint scalar radiation. Our second result is an extension of the classical double copy to spinning sources. Here, we compute. to linear order in spin. Yang -Mills radiation generated by a system of spinning color charges with chromoniagnetic spill dipole couplings. Using the same color-kinematic replacements, we show that it maps to classical gravitational radiation emitted by a system of interacting spinning masses. If this classical double copy correspondence persists to higher orders in perturbation theory. it suggests the possibility of vastly simplifying the calculation of gravitational radiation, in particular. that from colliding compact objects. recently discovered by LIGO.

Dissertations & Theses @ Yale University.

Books / Online / Dissertations & Theses

English

August 21, 2019

Thesis (Ph.D.)--Yale University, 2018.

Yale University.