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Publication Date

2023-5

First Advisor

Gary N. Felder

Second Advisor

William A. Loinaz

Document Type

Honors Project

Degree Name

Bachelor of Arts

Department

Physics

Keywords

particle physics, high-energy physics, Hamiltonian truncation, Rayleigh-Ritz method, numerical methods, strongly coupled quantum field theory, supersymmetric quantum mechanics, scattering theory, scattering matrix, S-matric, phase function

Abstract

Quantum mechanics and quantum field theory are fundamental frameworks of modern theoretical physics. Since their development in the early 20th century, physicists have long taken endeavors to use those frameworks to better describe our known physical universe. Many theories have been proposed and are awaiting confirmation, but their complex mathematical structures have hindered quick comparison with experiments. Thus a new movement in theoretical physics was embarked on, to develop methods to study complicated theories more accurately and faster and to yield accurate theoretical predictions to be directly tested against experimental data. Hamiltonian truncation (HT) is a product of this crucial movement and a methodology developed to complement more traditional methods used in quantum mechanics and quantum field theory. This Thesis is an exploration of this relatively new method and an attempt to apply this method to the study of scattering processes, for which it has been rarely employed to this date. This Thesis focuses on implementing HT in quantum mechanics, specifically, in onedimensional quantum mechanics and two-dimensional supersymmetric quantum mechanics. Following the procedure developed by Balthazar et al. [1], we numerically compute Hamiltonian matrices and use their eigenvalues to approximate scattering phase functions. We then analyze the spectrum, decay width, and lifetime of metastable states (resonances) and assess the effectiveness of HT in terms of the parameter L, the IR cutoff. For supersymmetric quantum mechanics, we confirm that our implementation of HT successfully reproduces the results by Balthazar et al. [1]. This Thesis lays the groundwork for future projects on HT that aim to implement the method in various quantum systems and to study more sophisticated scattering processes such as large multiparticle production in scalar quantum field theory.

Rights

©2023 Hyo Jung Park. Access limited to the Smith College community and other researchers while on campus. Smith College community members also may access from off-campus using a Smith College log-in. Other off-campus researchers may request a copy through Interlibrary Loan for personal use.

Language

English

Comments

[4] 38, iii pages: color illustrations, charts. Includes bibliographical references (pages 38-i).

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