Quantum Field Theory 2
A.Y. 2024/2025
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.
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 analyticity: Källen-Lehmann spectral representation, the optical theorem, Cutkosky rules, decay amplitues.
2. Ward identities: two-point Green's function, path integral derivation, examples.
3. Spontaneous symmetry breaking: symmetry breaking in classical field theory, Goldstone's theorem, effective potential.
4. Gauge invariance: Abelian and non-Abelian gauge theories in classical field theories.
5. Quantization of gauge theories, Fadeev-Popov terms.
6. Spontaneous symmetry breaking in quantum field theories with Abelian and non-Abelian gauge symmetries.
7. Renormalization: renormalization of QED, running coupling, renormalization group equation, operator product expansion, Callan-Symanzik equation
8. Chiral anomaly: conservation of axial current and chiral anomaly
2. Ward identities: two-point Green's function, path integral derivation, examples.
3. Spontaneous symmetry breaking: symmetry breaking in classical field theory, Goldstone's theorem, effective potential.
4. Gauge invariance: Abelian and non-Abelian gauge theories in classical field theories.
5. Quantization of gauge theories, Fadeev-Popov terms.
6. Spontaneous symmetry breaking in quantum field theories with Abelian and non-Abelian gauge symmetries.
7. Renormalization: renormalization of QED, running coupling, renormalization group equation, operator product expansion, Callan-Symanzik equation
8. Chiral anomaly: conservation of axial current and chiral anomaly
Prerequisites for admission
Knowledge of special relativity, quantum mechanics, and classical field theory, as well as quantum field theory as taught in the course Theoretical Physics I.
Teaching methods
The course consists of blackboard lectures in which the topics included in the syllabus will be presented. Interaction with the students in class is very much encouraged, through questions and discussions.
Teaching Resources
M.E. Peskin, D.V. Schroeder: An introduction to Quantum Field Theory; Addison-Wesley, 1995 (reference textbook)
T.P. Cheng, L.F. Li, Gauge Theory of Elementary Particle Physics; Oxford University Press, 1985 (for special topics)
S. Coleman: Aspects of Symmetry; Cambridge University Press, 1985 (for special topics)
R. Jackiw: Topological Investigations of Quantized Gauge Theories: in Current Algebra and Anomalies; Princeton University Press, 1985 (for special topics)
A. Zee, Quantum Field Theory in a Nutshell; Princeton University Press, 2010 (for extra insight, especially at a conceptual and qualitative level)
S. Weinberg: The Quantum Theory of Fields: Vol. I (foundations); Cambridge University Press, 1995 (for extra insight, especially at a more advanced and formal level)
T.P. Cheng, L.F. Li, Gauge Theory of Elementary Particle Physics; Oxford University Press, 1985 (for special topics)
S. Coleman: Aspects of Symmetry; Cambridge University Press, 1985 (for special topics)
R. Jackiw: Topological Investigations of Quantized Gauge Theories: in Current Algebra and Anomalies; Princeton University Press, 1985 (for special topics)
A. Zee, Quantum Field Theory in a Nutshell; Princeton University Press, 2010 (for extra insight, especially at a conceptual and qualitative level)
S. Weinberg: The Quantum Theory of Fields: Vol. I (foundations); Cambridge University Press, 1995 (for extra insight, especially at a more advanced and formal level)
Assessment methods and Criteria
An oral examination of approximately one hour, consisting of a presentation (approximately 30 minutes) by the student on a topic selected from those in the syllabus, by the professors. During the exam, the student will be asked a number of question which aim to ascertain their understanding of the topics covered in the course and their ability to apply these concepts in the more general context of quantum field theory.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 42 hours
Professor:
Röntsch Raoul Horst
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