TFNPV0007 Groups and Symmetries in Particle Physics

Institute of physics in Opava
winter 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Mikuláš Gintner, Ph.D. (lecturer)
prof. Ing. Peter Lichard, DrSc. (lecturer)
RNDr. Mikuláš Gintner, Ph.D. (seminar tutor)
RNDr. Josef Juráň, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Josef Juráň, Ph.D.
Institute of physics in Opava
Timetable
each odd Tuesday 13:05–14:40 425, each odd Tuesday 17:15–18:50 425
  • Timetable of Seminar Groups:
TFNPV0007/A: each odd Tuesday 14:45–16:20 425, each odd Wednesday 11:25–13:00 425, M. Gintner
Prerequisites (in Czech)
(FAKULTA(FU) && TYP_STUDIA(N))
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This lecture is primarily designed for the students of particle physics. Its main goal is to provide the mathematical foundation for the study of Quantum Field Theory and its applications in particle physics with the focus on the Lie groups and their representations.
Learning outcomes
Upon successful graduation from the subject, a student will be able to use the group theory in framework of physical theories.
Syllabus
  • The subject covers the following topics:
  • Introduction to the theory of Lie groups and their representations. Lie algebra.
  • The rotational group. Infinitesimal transformations. Ireducible representations of SO(3) and SU(2). Matrix representations of the rotational operators. Addition of the angular momenta and the Clebsch-Gordan coefficients.
  • Homogenous Lorentz group. Its fundamental properties. Lie algebra and irreducible representations.
  • Poincaré transformations. Group properties. Unitary representations.
  • Discrete transformations. Parity, charge conjugation, and time inversion.
  • Unitary symmetry. The U(1) symmetry and aditive quantum numbers. Isospin and isospin classification of hadrons. SU(3) group and its algebra, irreducible representations.
  • The gauge symmetry. Spontanous symmetry breaking.
  • The groups of the grand unification.
  • Supersymmetries.
Literature
    required literature
  • Costa G., Fogli G.: Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries. Springer, 2012. ISBN-13: 978-3642154812.
  • Vergados J. D.: Group and representation theory. World Scientific, 2017. ISBN 978-981-3202-44-3.
    recommended literature
  • Ramond P.: Group Theory: A Physicist's Survey. Cambridge, 2010. ISBN-13: 978-0521896030.
  • Georgi H.: Lie Algebras In Particle Physics: from Isospin To Unified Theories. CRC Press, 2018. ISBN-13: 978-0738202334.
Teaching methods
Monological (lecture, briefing)
Tutorial
Students' self-study
One-to-One tutorial
Assessment methods
homework
random test
written test
oral and written exam
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms winter 2020, winter 2021, winter 2023, winter 2024.
  • Enrolment Statistics (winter 2022, recent)
  • Permalink: https://is.slu.cz/course/fu/winter2022/TFNPV0007