Lecture and tutorials: Wed 13:10-16:20 lecture room T8 in Troja Lecturer: Karel Houfek.
Below you will find notes for each lecture. If you want to see what the lecture will be about, see my website from last year (in Czech), where you can also find scanned notes that I used last year. Or you can look at the lecture synopsis by doc. Kolorenč who taught this course in English in year 2021/2022.
| Date | Contents of the lecture/tutorial and scanned notes |
| 1.10. |
Basic concepts: group, rearrangement theorem, subgroups, generators, cosets, Lagrange theorem
(English notes, Czech notes) Tutorial: point groups for molecules (English notes, Czech notes), for examples of molecular symmetry groups see Symmetry@Otterbein |
| 8.10. | Basic concepts: cogjugacy classes, normal subgroups, direct and semidirect products, homomorphism (English notes, Czech notes) |
The condition to obtain credits is to get at least 40 points from homework assignments on finite groups (maximum is 60 points) and 20 points from homework assignments on Lie groups (maximum is 30 points). The number of points for individual problems is stated directly in the assignments.
You can submit assignments either via SIS (preferred method, ideally in PDF format), or in person on paper and exceptionally by email (if uploading to SIS fails).
Problems for year 2025/2026
Finite groups:
Individual topics are examined to the extent in which they were presented in lectures. As for the examples solved in lectures/exercises, it is sufficient to understand them as illustrations of the general theory, without detailed calculations and derivations.
The books (or articles) listed below are available for download in a "secret" subdirectory, the name of which you will learn at the lecture or upon request by sending an e-mail to the lecturer.
There is a lot of textbooks on groups in physics and the lectures do not follow any particular one. Therefore, it is really difficult to recommend one or two books that would cover everything. Browse (at least virtually) the books listed below and find the one that suits you most. Personally, I consider the books by Cornwell or Elliott and Dawber to be good overviews. For a geometric approach to Lie groups, I recommend Isham, although (unlike Fecko) there is no theory of representations.
Literature used in the preparation of the lecture
[1] Litzman, Otto a Sekanina, Milan:
Užití grup ve fyzice, Academia, Praha 1982 (in Czech)
[2] Hamermesh, Morton:
Group Theory and its Application to Physical Problems, Addison-Wesley 1962
[3] Sternberg, Shlomo:
Group Theory and Physics, Cambridge, 1994
[4] Fecko, Marián:
Diferenciálna geometria a Lieove grupy pre fyzikov, IRIS, Bratislava 2004, zvláště kap. 10-12
[5] Isham, Chris J.:
Modern Differential Geometry for Physicists, 2nd Ed, World Scientific, Singapore 1999, zvláště kap. 4
[6] Cornwell, J. F.:
Group Theory in Physics, Volumes I and II, Academic Press, London 1984
[7] Atkins, P.W., Child, M.S. a Phillips, C.S.G.:
Tables of Group Theory, Springer, Berlin, 1994
[8] Bishop, David M.:
Group Theory and Chemistry, Dover, New York, 1993
[9] Cotton, F. Albert:
Chemical Applications of Group Theory, 3rd Ed, John Wiley & Sons, New York 1990
[10] Elliott, J. P., Dawber, P. G.:
Symmetry in Physics, Volumes 1 and 2, MacMillan, London 1979
[11] Roman, Paul:
Advanced Quantum Theory, Addison-Wesley, Reading 1965, zvláště kap. 6
[12] Wigner, Eugene P.:
Group Theory, Academic Press, New York 1959
[13] Inui, T., Tanabe, Y., Onodera, Y.:
Group Theory and Its Application in Physics, Springer, Berlin 1996
[14] Ma, Zhong-Qi:
Group Theory for Physicists, World Scientific, New Jersey 2007
[15] Coleman, A. J.:
The Symmetric Group Made Easy in Advances in Quantum Chemistry 4 (1968) 83
[16] Wybourne, Brian G.:
Classical Groups for Physicists, John Wiley & Sons, New York 1974
[17] Greiner, Walter a Müller, Berndt:
Quantum Mechanics, Symmetries, 2nd Ed, Springer, Berlin, 1994