Line bundles and integrality conditions in quantum mechanics and quantum field theory
Choi, Dae Gyu
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https://hdl.handle.net/2142/23917
Description
Title
Line bundles and integrality conditions in quantum mechanics and quantum field theory
Author(s)
Choi, Dae Gyu
Issue Date
1988
Doctoral Committee Chair(s)
Kogut, John B.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
line bundles
integrality conditions
quantum mechanics
quantum field theory
curvature terms
flat connection terms
torsion
Language
en
Abstract
A complete theory for the line bundle structure in quantum mechanics and quantum field theory is given. This includes a general method for constructing curvature terms and flat connection terms. The necessary and sufficient condition for the existence of the integrality condition is obtained. The role of torsion parts in the first homology group of the configuration space is clarified. A possible extension to the higher dimensional vector bundle and its physical meanings are considered, too. Finally many physically interesting applications are given to illustrate our theory_ In particular, the local and global anomalies and other related topics including Berry's phase are discussed.
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