Line Bundles and Integrality Conditions in Quantum Mechanics and Quantum Field Theory.
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.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1988
- Bibcode:
- 1988PhDT........87C
- Keywords:
-
- Physics: Elementary Particles and High Energy