Fermions in Yang-Mills gauge theories: invariance, covariance, and topology
Invariance and covariance properties of the Dirac operator describing fermions in Yang-Mills fields are presented. This includes the study of anomalies of the gauge currents. The author was particularly interested in the geometric and topological features in the problem. The complicated topological structures and properties present in these theories are made clear by elementary calculations in several simple models. It is shown explicitly how nontrivial phase and sign ambiguities arise to give the so-called anomalies. The Atiyah-Singer index theorem is seen to be a very-powerful tool to calculate the topological invariants that characterize the anomalies. The index theorem also gives topological invariants describing the failure of covariance of the fermion propagator.
- Research Organization:
- Virginia Polytechnic Inst. and State Univ., Blacksburg (USA)
- OSTI ID:
- 7186524
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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