ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
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)
The objective of this course is to provide students with mathematical tools that will help them understand current theories of fundamental interactions and, more specifically, gauge theories and gravity. Therefore the main objectives of the course are to familiarize students with the main concepts of Lie algebras and their representations, as well as the main ideas of differential geometry of varieties. It is intended that at the end of the course students will acquire a practical knowledge of Lie algebras (especially SU (2) and SU (3)) of differential forms and the basic geometry of Riemann.
Learning results:
- To acquire a working knowledge of Lie algebras, especially in relation to their physical applications.
- To become familiar with the basic concepts of differential geometry of varieties and Riemann geometry.
- Groups and Lie algebras. Algebras SU (2) and SU (3). Semisimple Lie algebras. Cartan subalgebras and root systems.
- Theory of representations of SU (2). Weight systems. Representations of SU (N). Young diagrams and Clebsch-Gordan series. Application to the quark model.
- Lorentz and Poincare groups. Pauli-Lubanski vector and classification of representations.
- Elements of differential geometry of varieties. Vectors and tensors. Differential forms.
- Riemann Geometry. Parallel transport. Curvature. Application to general relativity.
-P. Ramond, Group theory, Cambridge U. P., 2012.
- J. Stillwell, Naive Lie Theory, Springer, 2008.
- B. Hall, Lie groups, Lie algebras and representations, Springer, 2003.
- M. Nakahara, Geometry, topology and Physics, Adam-Hilger, 2003.
- T. Frankel, The geometry of Physics, Cambridge U. P., 2004.
- S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press 1962.
On-line resources:
Both teaching material prepared by the teachers of the course and freely available on-line resources (links to books without author's rights, lecture notes) will be placed on the Virtual Classroom (=Aula Virtual).
NOTE: The USC is going to acquire electronic teaching material. The teachers of the course will specify the relevant material at the Virtual Classroom once it is avaliable.
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.
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.
The specific competences for this subject are:
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.
CE08-- Acquire an in-depth knowledge of the structure of matter in the low and high energy regime and its characterization .
The classes will be given according to the official calendar of the Masters. In these classes the contents of the subject will be explained, using all media available and introducing exercises and illustrative problems and / or clarification of such contents . Different material will be provided to the students in order to clarify both the development of the theoretical statements and the exercises and problems. There will be self-assessment tests so that students can monitor the progress of their learning. They will have the appropriate tutorials.
-It is compulsory to attend lectures and interactive classes and to perform the exercises.
- Specific works will be proposed.
Activity Weight in overall score
Attending classes and performing exercises: 60%
Presentation of papers or projects: 40%
Exceptionally it may take a final examination of the subject
The total student work is around 75 hours, distributed as follows:
Theory 20 hours
Seminars 10 hours
Tutoring one hour
Personal work and other activities 44 hours
Attendance and active participation in class.
Elena Gonzalez Ferreiro
Coordinador/a- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881813979
- elena.gonzalez.ferreiro [at] usc.es
- Category
- Professor: University Professor
Christoph Adam
- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881814087
- christoph.adam [at] usc.es
- Category
- Professor: University Lecturer
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| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 5 |
| Tuesday | |||
| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 5 |
| Wednesday | |||
| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 5 |
| Thursday | |||
| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 5 |
| Friday | |||
| 12:00-13:00 | Grupo /CLE_01 | Spanish | Classroom 5 |
| 01.14.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |
| 06.25.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 5 |