Quantum Field Theory (QFT) is the language that describes a wide spectrum of physics. However, it is notoriously hard at strong coupling regime. We approach this problem in an old Quantum Mechanical method - keep a finite number of states and diagonalize the Hamiltonian as a finite-size matrix. To study a QFT, we take the Hamiltonian to be the Conformal Field Theory as the Ultraviolet fixed point of the theory's Renormalization Group Flow, deformed by a relevant operator. We use a recent framework known as the Lightcone Conformal Truncation (LCT), where we use conformal basis and lightcone quantization. As an application of the method, we study the two dimensional Supersymmetric (SUSY) Gross-Neveu-Yukawa Model. The model is expected to have a critical point in the universality class of tri-critical Ising model, a massive phase and a massless SUSY-breaking phase. We use the LCT to compute the spectrum and the spectral density of the theory at all couplings and map the entire phase diagram.

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<p> In his monograph [Ne], Nekovar studies cohomological invariants of big Galois representations and looks at the variations of Selmer groups attached to intermediate number fields in a commutative p-adic Lie extension. In view of the formulation of the "main conjecture" for noncommutative extensions, it seems natural to extend the theory to a noncommutative p-adic Lie extension. This thesis will serve as a first step in an extension of this theory, namely, we will develop duality theorems over a noncommutative p-adic Lie extension which are extensions of Tate local duality, Poitou-Tate global duality and Grothendieck duality. </p> / Thesis / Doctor of Philosophy (PhD)

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Enhanced field emission (EFE) presents the main impediment to higher acceleration gradients in superconducting niobium (Nb) radiofrequency cavities for particle accelerators. The strength, number and sources of EFE sites strongly depend on surface preparation and handling. The main objective of this thesis project is to systematically investigate the sources of EFE from Nb, to evaluate the best available surface preparation techniques with respect to resulting field emission, and to establish an optimized process to minimize or eliminate EFE. To achieve these goals, a scanning field emission microscope (SFEM) was designed and built as an extension to an existing commercial scanning electron microscope (SEM). In the SFEM chamber of ultra high vacuum, a sample is moved laterally in a raster pattern under a high voltage anode tip for EFE detection and localization. The sample is then transferred under vacuum to the SEM chamber equipped with an energy-dispersive x-ray spectrometer for individual emitting site characterization. Compared to other systems built for similar purposes, this apparatus has low cost and maintenance, high operational flexibility, considerably bigger scan area, as well as reliable performance. EFE sources from planar Nb have been studied after various surface preparation, including chemical etching and electropolishing, combined with ultrasonic or high-pressure water rinse. Emitters have been identified, analyzed and the preparation process has been examined and improved based on EFE results. As a result, field-emission-free or near field-emission-free surfaces at ~140 MV/m have been consistently achieved with the above techniques. Characterization on the remaining emitters leads to the conclusion that no evidence of intrinsic emitters, i.e., no fundamental electric field limit induced by EFE, has been observed up to ~140 MV/m. Chemically etched and electropolished Nb are compared and no significant difference is observed up to ~140 MV/m. To address concerns on the effect of natural air drying process on EFE, a comparative study was conducted on Nb and the results showed insignificant difference under the experimental conditions. Nb thin films deposited on Cu present a possible alternative to bulk Nb in superconducting cavities. The EFE performance of a preliminary energetically deposited Nb thin film sample are presented. / Ph. D.