ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Particle Physics
Areas: Theoretical Physics
Center Faculty of Physics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Relativistic quantum field theories provide the basic tools to formulate the standard model of fundamental interactions of Nature. The main objective of this course is to introduce the concepts needed to study gauge theories in general, and more specifically the electroweak Glashow-Weinberg-Salam theory and quantum chromodynamics (QCD). We will introduce the Feynman path integral formulation of quantum field theories, and use it to discuss the quantization of gauge theories, spontaneous symmetry breaking, and renormalization.
- Path integral in quantum mechanics and quantum field theory. Generating functional and perturbative expansion.
- Gauge theories. Classical action and quantization. Fadeev-Popov ghosts and Feynman rules.
- Spontaneous symmetry breaking. Hidden symmetries. Goldstone theorem. Higgs mechanism.
- Renormalization. Ultraviolet and infrared divergencies. Counterterms and BPHZ method. Classification of theories. Dimensional regularization.
- Renormalization of quantum electrodynamics (QED). Vacuum polarization. Electron selfenergy. Vertex function and anomalous magnetic moment. Radiative corrections.
- The renormalization group. Equations of the renosmalization group. Beta function. Anomalous dimensions. Asymptotically free theories.
- M. Peskin, D. Schroeder, An introduction to quantum field theory, Addison-Wesley, 1995.
- M. Srednicki, Quantum Field Theory , Cambridge University Press, 2007
- S. Weinberg, The quantum theory of fields (vols. 1, 2), Cambridge University Press, 1995.
- C. Itzykson, J. B. Zuber, Quantum field theory, McGraw-Hill 1964.
- M. Le Bellac, Quantum and statistical field theory, Claredon Press-Oxford, 1991.
- S. Pokorski, Gauge field theories, Cambridge University Press, 1987.
Additional bibliography and online resources:
- https://www.damtp.cam.ac.uk/user/tong/qft.html
- https://www.thphys.uni-heidelberg.de/~weigand/QFT2-14/SkriptQFT2.pdf
- http://www.theory.caltech.edu/~preskill/notes.html
Students will acquire and practice basic and transversal competencies, common to all the subjects of the master,like the following:
CG01 - Acquire the ability to perform team research work.
CG02 - Be able to analyze and synthesize.
CG03 - Acquire the ability to write texts, articles or scientific reports according to publication standards.
CG04 - Become familiar with the different modalities used to disseminate results and disseminate knowledge in scientific meetings.
CG05 - Apply knowledge to solve complex problems.
CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context
CB7 - Knowledge about how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study
CB8 - Ability to integrate knowledge and face the complexity of making judgments based on information
that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments
CB9 - Ability to communicate conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way
CB10 - Learning skills allowing to continue studying in a way that will be largely self-directed or autonomous.
The specific competences for this subject are:
CE06 - Become familiar with the standard model of fundamental interactions and their possible extensions.
CE07 - Acquire the training for the use of the main computational tools and the management of the main experimental techniques of Nuclear and Particle Physics.
Transversal competences are
CT01 - Ability to interpret texts, documentation, reports and academic articles in English, scientific language par excellence.
CT02 - Develop the capacity to make responsible decisions in complex and / or responsible situations.
Learning outcomes:
Relativistic quantum field theories are the basic substrate of the standard model of the fundamental interactions of Nature. The objective of this course is to introduce the necessary concepts for the study of gauge theories in general and, more specifically, quantum electrodynamics, the unified electroweak theory of Glashow-Weinberg-Salam, and quantum chromodynamics. The fundamental tool employed in the course is the Feynman path integral. Using these functional techniques, the quantization of gauge theories, the mechanism of spontaneous symmetry breaking, and renormalization will be studied.
A course in the Moodle platform in the Virtual Campus will be activated, where useful information and teaching material will be uploaded.
The contents of this course will be introduced in the lectures according to the official calendar of the Máster, where exercises and problems will be proposed. The students will be provided with the required material both to follow the theoretical content and to solve the exercises and problems.
Individual sessions with the professor will be either remote or in person, if remote they will require booking which is also advised for the ones in person.
1) Assessment will be continuous by taking into account the following aspects:
-It will be compulsory to attend all the lectures and to solve the proposed exercises.
-The students will have to develop specific projects where they will put in practice the concepts, methods and techniques learned during the course. Depending on the interests of each student, these projects could be related to other subjects in the Master.
-Exceptionally, there could be a final exam if by any circumstance the previous activities do not allow an accurate evaluation of the performance of the students.
2) Relative weight of these activities in the global evaluation:
-Active participation in lectures and solving exercises: 60%
-Specific projects: 40%
-Final exam (exceptionally).
Unethical conduct during any exercise or exam required for the assessment of the subject will imply the failure to pass that subject, irrespective of other disciplinary measurements that can be prosecuted against the infractor. Unethical behaviour will include, among others, the elaboration of memories copied or obtained from publicly available sources without re-elaboration or reinterpretation, and without citation of authors and sources.
There will be 60 hours of lectures (40h of theoretical lectures and 20 hours of interacttive lectures)
It is rather difficult to estimate the amount of time need to assimilate this subject (actually any subject!) since it depends on the dedication and capabilities of each student. Nevertheless, we could estimate the study time in 90 hours in total.
Active participation in lectures, solve the propose exercises, and make use of tutorials.
Carlos Miguel Merino Gayoso
- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881813993
- carlos.merino [at] usc.es
- Category
- Professor: University Lecturer
Nestor Armesto Perez
Coordinador/a- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881814107
- nestor.armesto [at] usc.es
- Category
- Professor: University Professor
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| 16:00-17:15 | Grupo /CLE_01 | Spanish | Classroom B |
| Wednesday | |||
| 16:00-17:15 | Grupo /CLE_01 | Spanish | Classroom B |
| Thursday | |||
| 16:00-17:15 | Grupo /CLE_01 | Spanish | Classroom B |
| Friday | |||
| 16:00-17:15 | Grupo /CLE_01 | Spanish | Classroom B |
| 01.23.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 5 |
| 06.19.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |