Quantum Field Theory 2
A.Y. 2026/2027
Learning objectives
Expand the core ideas of relativistic quantum field theory which have been introduced in Quantum Field Theory 1, specifically in what
concerns analiticity, symmetry and invariance
concerns analiticity, symmetry and invariance
Expected learning outcomes
At the end of this course the student:
1.Will be able to use unitarity and the optical theorem to understand the analytic properties of amplitudes;
2.Derive the Ward identities for symmetres realized in Wigner-Weyl form;
3.Prove Glodstone's theorem for spontaneously broken symmetries, both at the classical and quantum level;
4.Construct and compute the effective potential;
5.Quantize a gauge theory and derive its Feynman rules with various gauge choices
6.Construct a gauge theory with massive field via the Higgs mechanism;
7.Renormalize quantum electrodymanics perturbatively;
8.Understand the quantum breaking of classical symmetries related to scale invariance (including chiral anomalies);
9.Write donw and solve the Callan-Symanzik equation (renormalization group equation);
10.Compute the operator-product (Wilson) expansion and the anomaloud dimensions of operators entering it.
1.Will be able to use unitarity and the optical theorem to understand the analytic properties of amplitudes;
2.Derive the Ward identities for symmetres realized in Wigner-Weyl form;
3.Prove Glodstone's theorem for spontaneously broken symmetries, both at the classical and quantum level;
4.Construct and compute the effective potential;
5.Quantize a gauge theory and derive its Feynman rules with various gauge choices
6.Construct a gauge theory with massive field via the Higgs mechanism;
7.Renormalize quantum electrodymanics perturbatively;
8.Understand the quantum breaking of classical symmetries related to scale invariance (including chiral anomalies);
9.Write donw and solve the Callan-Symanzik equation (renormalization group equation);
10.Compute the operator-product (Wilson) expansion and the anomaloud dimensions of operators entering it.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. Unitarity and Causality: Analytic properties of amplitudes, spectral representation, analytic structure of LSZ formula.
2. Ward identities
3. ccccccc classical field theories, quantum field theories, effective action
4. Gauge invariance: abelian symmetries in classical theories, non-abelian symmetries.
5. Quantization of gauge theories: abelian and non-abelian symmetries, BRST symmetry
6. Spontaneous symmetry breaking in abelian and non-abelian gauge theories.
7. Renormalization: in phi-4 scalar theory and QED
8. Renormalization with spontaneous symmetry breaking: the sigma model.
9. Renormalization group: Callan-Symanzik equation and evolution of couplings
10. Operator product expansion: formalism and application to e-e+ annihilation
11. Anomalies: axial anomaly, chiral symmetries in QFT
2. Ward identities
3. ccccccc classical field theories, quantum field theories, effective action
4. Gauge invariance: abelian symmetries in classical theories, non-abelian symmetries.
5. Quantization of gauge theories: abelian and non-abelian symmetries, BRST symmetry
6. Spontaneous symmetry breaking in abelian and non-abelian gauge theories.
7. Renormalization: in phi-4 scalar theory and QED
8. Renormalization with spontaneous symmetry breaking: the sigma model.
9. Renormalization group: Callan-Symanzik equation and evolution of couplings
10. Operator product expansion: formalism and application to e-e+ annihilation
11. Anomalies: axial anomaly, chiral symmetries in QFT
Prerequisites for admission
A good knowledge of quantum mechanics, basic group theory, and special relativity, as well as the material covered in Theoretical Physics 1: quantization of scalar and spinor quantum fields theories, path integral formalization, the treatment of interacting fields and Feynman rules, basics of ultraviolet renormalization for scalar field theories.
Teaching methods
Lectures on the blackboard, consisting of explanations of concepts as well as calculations.
Teaching Resources
Reference textbook: "An Introduction to Quantum Field Theory" by Michael E. Peskin and Daniel v. Schroeder (Westview, 1995).
Other useful books include:
- "The Quantum Theory of Fields Vol I: Foundations" by Steven Weinberg (Cambridge University Press, 2005)
- "Quantum Field Theory" by Claude Itzykson and Jean-Bernard Zuber (Dover, 2005)
- "Quantum Field Theory" by Mark Srednicki (Cambridge University Press, 2007)
- "Aspects of Symmetry" by Sidney Coleman (Cambridge University Press, 1985)
Students are encouraged to consult a wide number of textbooks and lecture notes to gain different perspectives on the material covered in the course.
Other useful books include:
- "The Quantum Theory of Fields Vol I: Foundations" by Steven Weinberg (Cambridge University Press, 2005)
- "Quantum Field Theory" by Claude Itzykson and Jean-Bernard Zuber (Dover, 2005)
- "Quantum Field Theory" by Mark Srednicki (Cambridge University Press, 2007)
- "Aspects of Symmetry" by Sidney Coleman (Cambridge University Press, 1985)
Students are encouraged to consult a wide number of textbooks and lecture notes to gain different perspectives on the material covered in the course.
Assessment methods and Criteria
An oral exam of approximately 45 minutes, during which the student will discuss a topic covered in the course, chosen by the examiners. The examiners will ask additional questions to fully ascertain the student's knowledge of the topic.
PHYS-02/A - Theoretical Physics of Fundamental Interactions, Models, Mathematical Methods and Applications - University credits: 6
Lessons: 42 hours
Professor:
Röntsch Raoul Horst
Professor(s)