Course: 994DF - TEORIA DEI CAMPI III 2025

Section outline

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Contenuti del corso:

1. Introduzione ai gruppi e alle algebre di Lie.
2. Teorie di gauge non-abeliane: invarianza di gaugee derivata covariante, connessione, azione classica.
3. Quantizzazione di Faddeev-Popov per teorie di gauge non-abeliane e simmetria BRST.
4. Rinormalizzazione di teorie di gauge non-abeliane.
5. Funzione beta e gruppo di rinormalizzazione. Teorie QCD-like a basse energie.
6. Operatori di linea e gruppo di gauge: Wilson loops e 't Hooft lines.
7. Aspetti topologici: Spazio delle configurazioni di teorie non-abeliane, istantoni e termine theta nell’azione.
8. Higher form symmetries in Maxwell e YM.
9. Anomalie: concetto di anomalia, anomalia chirale, anomalia e integrale sui cammini.

1. Introduction to Lie groups and Lie algebras.
2. Non-abelian gauge theories: gauge invariance and covariant derivative, connection, classical action.
3. Line operators and gauge group: Wilson loops and 't Hooft lines.
4. Faddeev-Popov quantization of non-abelian gauge theories and BRST symmetry.
5. Renormalization of non-abelian gauge theories.
6. Beta function and renormalization group.QCD-like theories in the IR.
7. Topological aspects: configuration space of non-abelian gauge theories, instantons and theta-term.
8. Higher form symmetries in Maxwell and YM.
9. Anomalies: concept of anomaly, chiral anomaly, anomaly and path integral.

Testi:
PS: Michael E. Peskin, Dan V. Schroeder "An Introduction to Quantum Field Theory", Westview Press.
W: Steven Weinberg "The Quantum Theory of Fields II", Cambridge University Press.
N: V. Parameswaran Nair "Quantum Field Theory", Springer.
R: Pierre Ramond "Field Theory a Modern Primer", Westview Press.
T: David Tong "Gauge Theory", https://www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
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