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Title:  Two applications of Berry's phase in fermionic field theory 
Author(s):  Goff, William Eugene 
Doctoral Committee Chair(s):  Stone, Michael 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, General
Physics, Condensed Matter Physics, Elementary Particles and High Energy 
Abstract:  When quantized fermions are coupled to a background field, nontrivial effects may arise due to the geometry and/or topology of the space of background field configurations. In this thesis, two examples of Berry's geometrical phase in a fermionic sea are studied: the anomalous commutator in gauge field theory and the intrinsic orbital angular momentum in superfluid $\sp3$HeA. Chapter 1 is a brief introduction. Chapter 2 reviews Berry's Phase and several toy models. Effective actions are calculated for two models in gradient expansions and the role of a geometric term is discussed. Chapter 3 investigates the anomalous commutator in the generators of gauge symmetry in field theory. Using an idea introduced by Sonoda, the Berry phase of the vacuum state is found to be the sum of the Berry phases of the individual states in the sea plus a piece due to the infinite nature of the Dirac sea. The latter is the anomalous commutator. Also found is a relative minus sign between the commutator of the total gauge symmetry generators and the commutator of the fermionic charge generators. Examples are given. In Chapter 4, a geometric way of deriving the intrinsic orbital angular momentum term in the $\sp3$HeA equations of motion is presented. Homogeneous, adiabatically evolving textures at zero temperature are found to pick up a nonzero groundstate Berry phase, where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting the phase as a WessZumino effective action for the condensate provides a geometric origin for the intrinsic angular momentum. The idea of a groundstate phase is then extended to other gap functions and a more general result is obtained. Chapter 5 concludes with a discussion of the possibility of unifying the two problems in a more general framework and directions for further work. 
Issue Date:  1989 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/20709 
Rights Information:  Copyright 1989 Goff, William Eugene 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9010865 
OCLC Identifier:  (UMI)AAI9010865 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics