Anomalies of a Weyl fermion in a gauge background

In this thesis we study the anomalies of a Weyl fermion in an abelian gauge back- ground. It is well-know that this model has a chiral anomaly which breaks the gauge invariance and prevents a consistent quantization of the corresponding gauge theory. In addition, there is a trace anomaly, whose precise structure is the main focus of the present study. We describe a derivation of these anomalies in terms of Feynman diagrams computa- tion, using dimensional regularization and the Breitenlohner-Maison scheme for treating the chiral matrix γ5. The issue discussed here is analogous to the one present in the context of a Weyl fermion coupled to a gravitational background. In that case, there has been recently a debate about the presence or absence of a contribution of a parity-odd term in the trace anomaly. The coupling of the Weyl fermion to an abelian gauge field provides a simpler setting for discussing the possible presence or absence of a parity-odd term in the trace anomaly. Our final result indicates that parity-odd terms do not arise.