Fermions in Yang-Mills gauge theories: invariance, covariance and topology

I present a study on the invariance and covariance properties of the Dirac operator describing fermions in Yang-Mills fields. This includes the study of anomalies of the gauge currents. We are 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. We show explicitly how non-trivial 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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Department dc:contributor.department

Physics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1987

Author dc:creator

• Liang, Yigao

Chair dc:contributor.committeechair

• Chang, Lay Nam

Committee members dc:contributor.committeemember

• Marshak, Robert E.
• Mo, Luke W.
• Roper, L. David
• Williams, Clayton D.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/77824

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/77824