Quantum Field Theory 2
A.Y. 2022/2023
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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: non-Abelian gauge theories, quantization of gauge theories, Fadeev-Popov terms, Higgs mechanism.
5. Renormalization: renormalization of QED, running coupling, renormalization group equation, operator product expansion
6. 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: non-Abelian gauge theories, quantization of gauge theories, Fadeev-Popov terms, Higgs mechanism.
5. Renormalization: renormalization of QED, running coupling, renormalization group equation, operator product expansion
6. Chiral anomaly: conservation of axial current and chiral anomaly
Prerequisites for admission
Knowledge of the basics of relativistic quantum field theory, special relativity and path integral methods as covered in the Quantum Field Theory I course.
Teaching methods
The course consists of blackboard lectures. Interactions with students, through questions and discussions, is encouraged.
Teaching Resources
Reference textbook: M. E. Peskin and D. V. Schroeder, "Introduction to Quantum Field Theory", Westview
Other useful textbooks:
- C. Itzykson and J.-B. Zuber, "Quantum Field Theory", Dover
- S. Weinberg, "The Quantum Theory of Fields, Vol. I", Cambridge University Press
- M. Srednicki, "Quantum Field Theory", Cambridge University Press
- S. Coleman, "Quantum Field Theory: Lectures of Sidney Coleman" (Ed. B. G.-g. Chen et. al.), World Scientific
Other useful textbooks:
- C. Itzykson and J.-B. Zuber, "Quantum Field Theory", Dover
- S. Weinberg, "The Quantum Theory of Fields, Vol. I", Cambridge University Press
- M. Srednicki, "Quantum Field Theory", Cambridge University Press
- S. Coleman, "Quantum Field Theory: Lectures of Sidney Coleman" (Ed. B. G.-g. Chen et. al.), World Scientific
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. 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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