Semiclassical Methods in Field Theories: The Use of Soliton and Instanton

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hsu, Yupai

• Physics, Elementary Particles and High Energy

Language dc:language

eng

Identifier

(UMI)AAI8108546

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/77195