## Geometrical aspects of gauge theories

### Prof. Cesare Reina

Content:

- Vector bundles. Metrics, connections and curvature.
- The space of connections and the Yang-Mills functional.
- The group of gauge transformations and its action on the space of connections. The orbit spaces.
- Gauge fixing and the Gribov ambiguity.
- The Faddeev-Popov method.
- Determinant of the chiral Dirac operator and anomalies.

References:

- Eguchi, Gilkey, Hanson, Phys.Rep. 66 (1980) 213-393
- Singer, Commumn. Math. Phys. 60 (1978) 7-12
- Freed, Uhlenbeck, Instantons and four-manifolds, Springer (1984)
- Donaldson, Kronheimer, The geometry of four-Manifolds, Claredon (1990)