Two applications of Berry's phase in fermionic field theory
Goff, William Eugene
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/23946
Description
Title
Two applications of Berry's phase in fermionic field theory
Author(s)
Goff, William Eugene
Issue Date
1989
Doctoral Committee Chair(s)
Stone, Michael
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Berry's phase
Fermionic field theory
Berry's geometrical phase
fermionic sea
anomalous commutator
intrinsic orbital angular momentum
superfluid
Language
en
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 superftuid 3He-A.
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 3He-A equations of motion is presented. Homogeneous, adiabatically evolving
textures at zero temperature are found to pick up a nonzero ground-state Berry phase,
where the ground state is taken to be a filled sea of Bogoliubov quasiparticles. Interpreting
the phase as a Wess-Zumino effective action for the condensate provides a geometric origin
for the intrinsic angular momentum. The idea of a ground-state 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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
