Semiclassical Methods in Field Theories: The Use of Soliton and Instanton
Hsu, Yupai
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https://hdl.handle.net/2142/77195
Description
Title
Semiclassical Methods in Field Theories: The Use of Soliton and Instanton
Author(s)
Hsu, Yupai
Issue Date
1980
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Elementary Particles and High Energy
Language
eng
Abstract
The first part of this thesis is to study how solitons interact among themselves in Sine-Gordon system. We translate the information encoded in various known soliton solutions such as scattering time delays and oscillation periods into that of the corresponding quantities in particle dynamics. We examine different points of view for obtaining the interaction potentials. We then quantize the effective potentials and compare the mass spectrum with that obtained from the path integral approximation. The second part of this thesis concerns with the instanton physics in Sigma model and in nonabelian gauge theory. An instanton solution defines a dominant collective coordinate. By considering only the quantum physics along these coordinates (a good approximation in weak coupling limit), we can reduce a complicated field theory problem to a simple Schrodinger type problem. We study the interaction among instantons, examine the dilute gas limit assumption, and compute the vacuum state wave functionals and eigen-energies. We also study the method to generate envelope solutions out of a family of existing instanton solutions.
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