- Lecture 1:Symmetries and classical conservation laws. Gauge transformations and conservation of currents. Vector current and axial current.
Amplitudes in Quantum Field Theory and quantum conservation laws: Ward identities. Generating functional for amplitudes (n-point Green functions).
- Lecture 2:The computations of ABJ anomaly: computations of divergencies for the vector and axial 3-point Green functions using Fourier
transform: managing the differences of divergent terms. Comparison with the regularized approach: Pauli-Villars and dimensional regularization.
- Lecture 3:Covariant regularisation: the assumptions. The explicit computation of the divergence of the regularized axial current. The
anomalous term. Grassman variables.
- Lecture 4:Path integral approach and the change of path integral measure under gauge transformations.
- Lecture 5:Gauge fixing and ghosts: the origins of BRST transformations.
- Lecture 6:Geometric form of anomalies: characteristic classes
- Lecture 7:Descent equations and Wess-Zumino consistency conditions.
- Lecture 8:Gravitational anomalies and anomaly cancellation in the Standard Model.
|
Mathematical methods in quantum field theory: anomalies
Problems to solve.