Degree | Type | Year | Semester |
---|---|---|---|
2500097 Physics | OT | 4 | 2 |
Recommendation: Quantum physics. Quantum mechanics and theoretical mechanics.
1. General motivation
2. Introduction (classical fields)
(a) Motivation for fields: Many body problems. One example
(b) Elements of classical field theory:
• Functional calculus (reminder)(c) Natural units
3. Non-relativistic Quantum Field Theory. Free fields
(a) Bosons. Fock space. Number operator (particle interpretation) and statistics. Connection with quantum mechanics
(b) Fermions. Fock space. Number operator (particle interpretation) and statistics. Connection with quantum mechanics
4. Poincare Group
(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 (*)
5. Interaction (scalar case)
(a) Cross Section and S matrix
(b) Interaction picture and S matrix
(c) Klein-Gordon real field. Propagator and causality
(d) Motivation for causal (free) fields
(e) Wick theorem
(f) Continuous symmetries Noether theorem: associated charges and currents. Energy-momentum tensor
(c) Klein-Gordon complex field. Charge symmetry. Antiparticle.
6. Quantum Electrodynamics (QED)
(a) Field for a massless spin-one particle: Electromagnetic field
(b) Dirac field: construction. Propagator, symmetries, spin: helicity and quirality. Spin-statistics theorem
(c) Quantization of QED
(d) S-matrix to O(e2). Feynman diagrams
(e) Compton scattering to tree level. Feynman diagrams and computational
techniques: traces, spin, ...
(f) Generalized Feynman rules
(g) About gauge invariance. Example of Ward identity (*)
(h) Other elementary processes of QED to tree level: e+e− → e+e−, e+e− →
μ+μ−, ...
(i) Decays. Radiative transitions of hydrogen
(j) Hydrogen-like atoms in Quantum Field Theory (*)
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 | |||
Problems class | 16 | 0.64 | 2, 1, 3, 4, 6, 7, 9, 14, 13, 12, 15, 17, 16 |
Theoretical classes | 33 | 1.32 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 8, 13, 12, 15, 17, 18, 16 |
Type: Autonomous | |||
Discussion, work in groups | 22 | 0.88 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 19, 8, 13, 12, 15, 17, 18, 16 |
Problems solved in group or autonomously | 30 | 1.2 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 19, 8, 13, 12, 15, 17, 18, 16 |
Study of theoretical foundations | 42 | 1.68 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 19, 8, 13, 12, 15, 17, 18, 16 |
1st partial exam: 50% of the grade.
2nd Partial exam: 45% of the grade.
Selective delivery of problems: 5% of the grade.
In order to be able to take part in the recovery exam, one should have been previously presented to both exams.
Examination of recovery of the two partials: 95% of the note. There is no minimum mark to be able to opt for the
recovery
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Exam 1 | 50% | 2 | 0.08 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 8, 10, 13, 12, 15, 17, 16 |
Exam 2 | 45% | 2 | 0.08 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 8, 13, 12, 15, 17, 16 |
Homework | 5% | 1 | 0.04 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 19, 8, 11, 10, 13, 12, 15, 17, 18, 16 |
resit exam | 95% | 2 | 0.08 | 2, 1, 3, 4, 5, 6, 7, 9, 14, 8, 13, 12, 15, 17, 16 |
• D. Lurie, Particles and Fields
• S. Weinberg, The Quantum Theory of Fields
• L.H. Ryder, Quantum Field Theory
• M. Peskin and D. Schroeder, An introduction to Quantum Field Theory
• B. Hatfield, Quantum Field Theory of Point Particles and Strings
• J.F. Donoghue, E. Golowich, B.R. Holstein, Dynamics of the Standard Model • S. Pokorsky, Gauge Field Theories
• C. Itzykson and J. Zuber, Quantum Field Theory
• F.J. Yndurain, Elements of grup theory. https://arxiv.org/pdf/0710.0468