Group Theory in Physics: Online Course by Prof. P. Ramadevi | IIT Bombay
Course Details
| Exam Registration | 56 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 12 weeks |
| Categories | Physics |
| Credit Points | 3 |
| Level | Undergraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 24 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Unlocking the Universe: A 12-Week Journey into Group Theory Methods in Physics
Have you ever wondered what fundamental principle connects the vibrations of a molecule, the classification of subatomic particles, and the very fabric of spacetime? The answer lies in symmetry, and the mathematical language to describe it is Group Theory. For physics students, mastering this language is not just an academic exercise; it's a key to unlocking deeper insights across nearly every field of modern physics.
We are excited to present a comprehensive 12-week course, "Group Theory Methods in Physics," instructed by Prof. P. Ramadevi from IIT Bombay. Designed for beginners at the undergraduate and postgraduate levels, this course bridges the gap between abstract mathematical concepts and their powerful applications in the physical world.
About the Course and Instructor
This course is meticulously structured to build your understanding from the ground up. You will start with the basics of discrete groups and progressively move towards advanced topics like Lie algebras and their pivotal role in particle physics. The goal is to ensure you not only learn the theory but also learn to appreciate its wide-ranging applications.
Your guide on this journey is Prof. P. Ramadevi, a renowned researcher in mathematical physics from IIT Bombay. With extensive research experience in areas like knot invariants from Chern-Simons theory and topological strings, Prof. Ramadevi brings a wealth of knowledge and a clear, application-oriented perspective to the teaching of group theory.
Who Should Take This Course?
- Intended Audience: Students with a background in Physics (UG/PG).
- Prerequisites: A working knowledge of Linear Algebra, Quantum Mechanics, and Special Theory of Relativity is required to fully engage with the course material.
- Industry Support: The tools taught in this course are highly valuable in Research & Development (R&D) departments across industries working in advanced materials, quantum computing, and fundamental research.
Detailed 12-Week Course Layout
Here is a week-by-week breakdown of what you will learn:
| Week | Topics Covered |
|---|---|
| Week 1 | Introduction to discrete groups, subgroups and generators, conjugacy classes |
| Week 2 | Symmetric groups, permutation group, cycle notation |
| Week 3 | Direct product groups, semi-direct product groups |
| Week 4 | Symmetries of molecules, point groups and stereographic projection |
| Week 5 | Matrix representation of groups, reducible and irreducible representation |
| Week 6 | Great orthogonality theorem and character tables, Mulliken notation, basis |
| Week 7 | Tensor product, projection operator, observables, selection rules, molecular vibrations |
| Week 8 | Continuous groups, generators, Lorentz transformation |
| Week 9 | Orthogonal groups and Lie algebra |
| Week 10 | Unitary groups, SU(2), SU(3), weight vector diagrams and root vector diagrams |
| Week 11 | Wigner-Eckart theorem, examples |
| Week 12 | Quark model, SU(3) baryons, mesons, Wigner-Eckart theorem, hydrogen atom, dynamical symmetry |
Key Learning Outcomes
By the end of this course, you will be able to:
- Analyze symmetries in physical systems using formal group theory.
- Construct and use character tables for point groups.
- Apply representation theory to solve problems in quantum mechanics and molecular physics.
- Understand the structure of Lie groups and algebras like SO(3), SU(2), and SU(3).
- Appreciate the foundational role of SU(3) in the quark model for classifying hadrons (baryons and mesons).
- Utilize powerful theorems like the Wigner-Eckart theorem to simplify calculations of matrix elements.
Recommended Textbooks
To supplement your learning, the following textbooks are highly recommended:
- Group Theory and its Applications to Physics Problems by Morton Hamermesh
- Lie Algebras in Particle Physics by Howard Georgi
- Group Theory for Physicists: With Applications by Pichai Ramadevi and Varun Dubey (A textbook co-authored by the instructor herself, ensuring perfect alignment with the course content).
Why is Group Theory Essential for a Physicist?
Group theory is the backbone of modern theoretical physics. It provides the framework to understand conservation laws (via Noether's theorem), classify elementary particles, simplify complex quantum mechanical problems, and describe the fundamental forces. From the crystal structure in condensed matter physics to the gauge theories of the Standard Model, symmetry principles formulated through group theory are everywhere. This course is your gateway to speaking this universal language of physics.
Embark on this 12-week journey to transform your understanding of physics. Enroll in "Group Theory Methods in Physics" and learn from one of the best, Prof. P. Ramadevi at IIT Bombay.
Enroll Now →