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Theory of groups for physics applications


Group Theory is the mathematics of symmetry. It is used extensively in quantum theory. There are applications to molecular structure, spectroscopy, crystal structure and to Elementary Particle physics

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Physics, Engineering Physics, Chemistry, Metallurgical Engineering, Materials science, Electrical engineering



PREREQUISITES: Multivariate calculus, Linear Algebra, Introductory Quantum Mechanics, Special Theory of Relativity

INDUSTRY SUPPORT: Materials technologies

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Faculty at IIT Bombay since 1989. Primary research interest in Elementary Particle Physics and Cosmology. Primary teaching interest mathematical and theoretical physics. I like to design instructional material so that the essentials of the advanced material become accessible to interested undergraduates


Week 1  : Introduction & Algebraic Preliminaries, Basic Group Concepts & low Order groups, Tutorial 1
Week 2  : Lagrange’s Theorem & Cayley’s Theorem, Factor Group Conjugacy Classes, Tutorial 2
Week 3  : Cycle Structures & Molecular Notation, Cycle Structures & Classification, Tutorial 3
Week 4  : Point Group Notation & Factor Group, Representation Theory -1, Tutorial 4
Week 5  : Representation Theory -2, Schur’s Lemma & Orthogonality Theorem, Tutorial 5
Week 6  : Orthogonality for Characters, Character tables & molecular Applications, Tutorial 6
Week 7  : Preliminaries  about the continuum, Classical Groups, Tutorial 7
Week 8  : Classical Groups -- Topology, SO(3) and Matrix Exponent, Tutorial 8
Week 9  : Generators, discussion of Lie’s theorems, Group Algebras;  SO(3)  SU(2) Correspondence, Tutorial 9
Week 10  : SO(3), SU(2)  Representations, Representation on Function Spaces, Tutorial 10
Week 11  : Lorentz Boosts;  SO(3,1) Algebra, Representation of Lorentz Group & Clifford Algebra, Tutorial 11
Week 12  : SU(3) and Lie’s classification, Fundamental symmetries of Physics, Tutorial 12


M S Dresselhaus, G Dresselhaus and A Jorio Applications of group theory to the physics of condensed matter (2008), Brian C Hall, Lie groups lie algebras and representations (2015),Morton Hammermesh Group theory and its applications to physical problems(1962)
  • The exam is optional for a fee.
  • Date and Time of Exam: October 28, 2018 (Sunday)
  • Time of Exams: Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm.
  • Exam for this Course will be available in both morning & afternoon sessions.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at http://nptel.ac.in/noc/