Degree | Type | Year | Semester |
---|---|---|---|
4313861 High Energy Physics, Astrophysics and Cosmology | OT | 0 | 1 |
It is recommended to have followed the course Introduction to the Physics of the Cosmos.
The main purpose of this course is to learn the basic concepts and techniques behind the theory of quantum fields, with aplications to elementary particle physics, in particular Quantum Electrodynamics.
1. Introduction
(a) Fock space. Asymptotic states
(b) Natural units
(c) Cross Section and S matrix
(d) Interaction picture and S matrix
(e) Decays
2. Poincare Group. Reminder
(a) Poincare group and Lorentz group.
(b) Associated Lie algebra.
(c) One particle irreducible representation. Wigner method. Little group.
Spin, helicity. Massive and massless case
(d) Discrete symmetries: C, P, T (*)
3. Interaction (scalar case)
(a) Klein-Gordon real field. Propagator and causality
(b) Motivation for causal (free) fields
(c) Wick theorem
(d) Continuous symmetries Noether theorem: associated charges and currents.
Energy-momentum tensor
(e) Klein-Gordon complex field. Charge symmetry. Antiparticle.
4. Quantum Electrodynamics (QED)
(a) Field for a massive spin-one particle: Proca field
(b) Field for a massless spin-one particle: Electromagnetic field
(c) SL(2,C) and non-unitary irreducible representations of the Lorentz group
(d) Dirac field: construction. Propagator, symmetries, spin: helicity and
quirality. Spin-statistics theorem
(e) Quantization of QED
(f) S-matrix to O(e^2).
• Elementary processes of QED to tree level: Compton scattering,
e+e− → e+e−, e+e− → μ+μ−, ...
• Feynman diagrams and computational techniques: traces, spin, ...
(g) About gauge invariance. Examples of Ward identity
(h) Generalized Feynman rules
(i) Soft Bremsstrahlung (*)
5. Beyond tree level. Introduction
(a) Infinities and dimensional regularization.
(b) Vacuum polarization.
(c) Renormalization of the electric charge.
(d) Optical theorem.
(e) Dispersion relations (*)
(f) Bound states in Quantum Field Theory: Hydrogen-like atoms (*)
(g) Renormalization of QED (*)
6. Beyond perturbation theory.
(a) LSZ formalism and crossing symmetry (examples).
There will be teaching lectures where the theory will be explained in detail.
There will be teaching lectures where a selection of the list of exercises will be discussed.
The student should digest at home the theory explained in class, and perform the list of exercises suggested during the lectures.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Theory and problems | 45 | 1.8 | 1, 2, 3, 4, 5 |
Type: Autonomous | |||
Study, exercises | 84 | 3.36 | 1, 2, 3, 4, 5 |
Exam: 50%
Exercises delivery: 40%
Pariticipation in class and oral presentation of some exercises: 10%
Make-up exam: 50%. Necessary condition: To have 3.5 or more in the previous final mark.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Exam | 50% | 3 | 0.12 | 1, 2, 3, 4, 5 |
Exercises delivery | 40% | 15 | 0.6 | 1, 2, 3, 4, 5 |
Oral presentations and active attendance in class | 10% | 3 | 0.12 | 1, 2, 3, 4, 5 |
D. Lurie. Particles and Fields
M. Peskin and D. Schroeder. An introduction to Quantum Field Theory
L.H. Ryder. Quantum Field Theory
S. Weinberg. The Quantum Theory of Fields
C. Itzykson and J. Zuber. Quantum Field Theory