Details of PH4213 (Spring 2025)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| PH4213 | Symmetry Methods in Physics | Ananda Dasgupta |
| Syllabus |
|---|
| 1. Basics of group theory: recapitulation of basic definitions. Normal subgroups and quotient groups. Isomorphism theorems. Direct and semi-direct product of groups.
2. Representation theory: linear and matrix representations. Function space representations. The regular representation. Unitary representations. Reducible and irreducible representations. Schurs lemmas. The Great Orthogonality Theorem. Orthogonality of character vectors. Irreducibility criterion. Reduction of representations. Projection operators. Wigner-Eckart theorem. 3. Continuous groups: SO(3) and SU(2). The connection between Lie Groups and Lie algebras. The representation theory of semi-simple Lie algebras. Roots and weights. Dynkin diagrams. 4. Representation theory of the symmetric group. Young tableaux. Their applications to the representations of SU(N). 5. Applications to various physical systems. These may include molecular vibrations, crystal field effects, identical particles, the quark model etc. |
| Prerequisite |
|---|
| Linear algebra and basics of group theory. Acquaintance with quantum mechanics (at the third year level) desirable. |
| References |
|---|
| Recommended books:
1. Thomas Wolfram, Sinasi Ellialtioglu - Applications of group theory to atoms, molecules, and solids , Cambridge University Press, 2014 2. J. P. Elliott and P. G. Dawber Symmetry in physics Vols. 1 and 2, McMillan Press 1979 3. Mildred S. Dresselhaus, Gene Dresselhaus, and Ado Jorio Group theory : Application to the Physics of Condensed Matter, Springer-Verlag, 2008 4. Pierre Ramond - Group Theory: A Physicist's Survey, Cambridge University Press, 2010 |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Elective |
| 2 | IP | 4 | Elective |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Not Allowed |
| 6 | MR | 2 | Elective |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |