Important notice
The course guide is provisional.
The PDF version of the course guide may take a few days to become available in the DDD.
Introduction to Quantum Field Theory
Code: 42863Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| High Energy Physics, Astrophysics and Cosmology | OP | 1 |
Contact lecturer
- Name :
- Antonio Miguel Pineda Ruiz
- Email :
- antoniomiguel.pineda@uab.cat
Teaching staff
- Antonio Miguel Pineda Ruiz
Group languages
You can consult this information at the end of the document.
Prerequisites
It is recommended to have followed the course Introduction to the Physics of the Cosmos, and be familiar with classical field theory and special relativity.
Objectives
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.
Learning outcomes
- CA05 (Adapt techniques on quantization and interaction to solve other quantum field theory problems.) Adapt techniques on quantization and interaction to solve other quantum field theory problems.
- KA04 (Identify the bases of quantum field theory.) Identify the bases of quantum field theory.
- KA05 (Summarize the concept of renormalization in quantum field theory.) Summarize the concept of renormalization in quantum field theory.
- SA10 (Apply quantum field theory to electromagnetic processes.) Apply quantum field theory to electromagnetic processes.
- SA11 (Apply the concept of renormalization to electromagnetic processes.) Apply the concept of renormalization to electromagnetic processes.
- SA12 (To analyze the concept of renormalization in quantum field theory.) To analyze the concept of renormalization in quantum field theory.
- SA13 (Apply the language of Feynman diagrams to quantum field theory.) Apply the language of Feynman diagrams to quantum field theory.
- SA14 (Use specialized bibliographic sources, scientific articles, and digital resources in English to delve into the concepts of quantum field theory and its applications in high-energy physics.) Use specialized bibliographic sources, scientific articles, and digital resources in English to delve into the concepts of quantum field theory and its applications in high-energy physics.
Contents
1. Introduction
(a) Fock space. Asymptotic states
(b) Poincare group and Lorentz group
(c) Associated Lie algebra
(d) One particle irreducible representation. Wigner method. Little group.
Spin, helicity. Massive and massless case
(e) Natural units
2. Interaction
(a) Cross Section and S matrix
(b) Decays and S matrix
(c) Interaction picture and S matrix
(d) Motivation for causal (free) fields
(e) Poincare symmetry and S matrix
(f) Wick theorem
3. Fields for particles with spin
(a) SL(2,C) and non-unitary irreducible representations of the Lorentz group (*)
(b) Dirac field: construction. Propagator, symmetries, spin: helicity and
quirality. Spin-statistics theorem
(c) Field for a massive spin-one particle: Proca field
(d) Field for a massless spin-one particle: Electromagnetic field
4. Quantum Electrodynamics (QED)
(a) Quantization of QED
(b) 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, ...
(c) Generalized Feynman rules
(d) About gauge invariance. Examples of Ward identity
(e) Non relativistic limit of QED
(f) 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 (*)
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Theory and problems | 45 | 1.8 | |
| Study, exercises | 84 | 3.36 |
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.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Exam | 50% | 3 | 0.12 | CA05, KA04, KA05, SA10, SA11, SA12, SA13, SA14 |
| Oral presentations and active attendance in class | 20% | 3 | 0.12 | CA05, KA04, KA05, SA10, SA11, SA12, SA13, SA14 |
| Exercises delivery | 30% | 15 | 0.6 | CA05, KA04, KA05, SA10, SA11, SA12, SA13, SA14 |
Exam: 50%; Retake exam: 50%.
Assignments: 30%
Class participation and oral presentation of some exercises: 20%
To pass the subject, you must have a grade equal to or greater than 2.5 in the exam, and the sum of all the assessment activities must add up to 5 or more.
This subject does not include a single assessment system.
In this course, the use of Artificial Intelligence (AI) technologies is not permitted at any stage. Any work containing AI-generated content will be considered a breach of academic integrity and may result in a partial or total grade penalty for the assignment, or more severe sanctions in serious cases.
Bibliography
• A. Pineda, Introduction to Quantum Field Theory
• A. Cornellà and J.I. Latorre, Teoria clàssica de camps
• D. Lurie, Particles and Fields
• S. Weinberg, The Quantum Theory of Fields
• L.H. Ryder, Quantum Field Theory
• F.J. Yndurain, Elements of grup theory. https://arxiv.org/pdf/0710.0468
• C. Itzykson and J. Zuber, Quantum Field Theory
• B. Hatfield, Quantum Field Theory of Point Particles and Strings
• S. Pokorsky, Gauge Field Theories
• M. Peskin and D. Schroeder, An introduction to Quantum Field Theory
• J.F. Donoghue, E. Golowich, B.R. Holstein, Dynamics of the Standard Model
Software
General calculus programs like Mathematica
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TEm) Theory (master) | 1 | English | first semester | morning-mixed |