Quantum Field Theory
- a.y. 2019/20 – 2023/24
- Master’s in Physics (LM)
- 1st year, 2nd semester
This course is no longer running; the page is kept as an archive.
General information
- Suggested course
- Theoretical Physics.
- Target skills and knowledge
- An introduction to the path-integral formulation of quantum field theories, to discuss their structural aspects. At the end of the course students should master the basic techniques to compute relevant quantities in quantum field theory using the path integral.
- Learning activities
- Lectures. Weekly assignments.
- Examination method
- Questions on the topics presented during the course and solution of a problem.
- Textbooks
- M. Srednicki, Quantum Field Theory, CUP.
- L. Brown, Quantum Field Theory, CUP.
- M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, 1995.
- S. Weinberg, The Quantum Theory of Fields, vols. I and II, CUP, 1995.
Class schedule
| Day | Time | Room |
|---|---|---|
| Monday | 8:30–10:15 | Aula P4C |
| Tuesday | 8:30–10:15 | Aula LuF |
Office hour: Fridays, 15:00–16:00, preferably by appointment (also by e-mail or telephone).
Syllabus
1. The LSZ reduction formula
1.1 A new approach to quantum field theory. 1.2 Correlators and the LSZ reduction formula.
2. The path integral in quantum mechanics
2.1 Intuitive introduction to path integrals. 2.2 From the Schrödinger equation to the path integral. 2.3 The partition function. 2.4 Operators and time ordering. 2.5 The continuum limit and non-commutativity.
3. Perturbation theory
3.1 Correlators and scattering amplitudes. 3.2 Free field theory. 3.3 Perturbation theory. 3.4 Feynman diagrams. 3.5 Borel resummation*. 3.6 Exact results: localization*.
4. Effective and quantum action
4.1 Wilsonian effective action. Integrating out fields. 4.2 The 1PI effective action.
5. Path-integral quantization of λφ⁴
5.1 Dimensional analysis. 5.2 The free theory. 5.3 The interacting theory. 5.4 The Coleman–Weinberg potential.
6. Quantising spin ½ and spin 1 fields
6.1 Path integral for Dirac fermions. 6.2 Path integral for photons.
7. Perturbative renormalization
7.1 Divergences. 7.2 Superficial degree of divergence and the BPHZ theorem. 7.3 One-loop propagator in λφ⁴. 7.4 On-shell renormalization. 7.5 Dimensional regularization. 7.6 λφ⁴ at two loops. 7.7 QED renormalization.
8. The renormalization group
8.1 Renormalization and integrating out degrees of freedom. 8.2 The Callan–Symanzik equations. 8.3 Anomalous dimensions. 8.4 Renormalization group flow. 8.5 Counterterms and the continuum limit. 8.6 Polchinski equations. 8.7 The local potential approximation. 8.8 Dimensional regularization. 8.9 The Gaussian critical point and Landau poles. 8.10 The Wilson–Fisher critical point. 8.11 Zamolodchikov’s c-theorem.
9. Symmetries
9.1 Slavnov–Taylor identities. 9.2 Schwinger–Dyson equation and Ward–Takahashi identities. 9.3 Ward identities for QED.
10. Quantization of non-abelian gauge theories
10.1 Classical Yang–Mills theories. 10.2 Quantization issues. 10.3 Faddeev–Popov determinant. 10.4 Ghosts. Nakanishi–Lautrup fields. 10.5 BRST symmetry. 10.6 BRST charge and physical Hilbert space.
Sections marked * are not part of the examination.
Exams
Written examination.