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Theory of Groups for Physics Applications. Instructor: Prof. Urjit A. Yajnik, Department of Physics, IIT Bombay.

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September 23, 2023

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September 23, 2023

Duration:

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FREE

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Description

Theory of Groups for Physics Applications. Instructor: Prof. Urjit A. Yajnik, Department of Physics, IIT Bombay.

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. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction Unlimited
  • Lecture 02 – Algebraic Preliminaries Unlimited
  • Lecture 03 – Basic Group Concepts and Low Order Groups Unlimited
  • Lecture 04 – Basic Group Concepts and Low Order Groups (cont.) Unlimited
  • Lecture 05 – Lagrange’s Theorem and Cayley’s Theorem Unlimited
  • Lecture 06 – Lagrange’s Theorem and Cayley’s Theorem (cont.) Unlimited
  • Lecture 07 – Factor Group Conjugacy Classes Unlimited
  • Lecture 08 – Factor Group Conjugacy Classes (cont.) Unlimited
  • Lecture 09 – Cycle Structures and Molecular Notation Unlimited
  • Lecture 10 – Cycle Structures and Molecular Notation (cont.) Unlimited
  • Lecture 11 – Cycle Structures and Classification Unlimited
  • Lecture 12 – Cycle Structures and Classification (cont.) Unlimited
  • Lecture 13 – Point Group Notation and Factor Group Unlimited
  • Lecture 14 – Point Group Notation and Factor Group (cont.) Unlimited
  • Lecture 15 – Representation Theory I Unlimited
  • Lecture 16 – Representation Theory II Unlimited
  • Lecture 17 – Representation Theory III Unlimited
  • Lecture 18 – Representation Theory IV Unlimited
  • Lecture 19 – Schur’s Lemma and Orthogonality Theorem Unlimited
  • Lecture 20 – Schur’s Lemma and Orthogonality Theorem (cont.) Unlimited
  • Lecture 21 – Orthogonality for Characters Unlimited
  • Lecture 22 – Orthogonality for Characters (cont.) Unlimited
  • Lecture 23 – Character Tables and Molecular Applications Unlimited
  • Lecture 24 – Character Tables and Molecular Applications (cont.) Unlimited
  • Lecture 25 – Preliminaries about the Continuum Unlimited
  • Lecture 26 – Preliminaries about the Continuum (cont.) Unlimited
  • Lecture 27 – Classical Groups Unlimited
  • Lecture 28 – Classical Groups (cont.) Unlimited
  • Lecture 29 – Classical Groups – Topology Unlimited
  • Lecture 30 – Classical Groups – Topology (cont.) Unlimited
  • Lecture 31 – SO(3) and Matrix Exponent Unlimited
  • Lecture 32 – SO(3) and Matrix Exponent (cont.) Unlimited
  • Lecture 33 – Generators, Discussion of Lie’s Theorems Unlimited
  • Lecture 34 – Generators, Discussion of Lie’s Theorems (cont.) Unlimited
  • Lecture 35 – Group Algebras; SO(3)-SU(2) Correspondence Unlimited
  • Lecture 36 – Group Algebras; SO(3)-SU(2) Correspondence (cont.) Unlimited
  • Lecture 37 – SO(3), SU(2) Representations Unlimited
  • Lecture 38 – SO(3), SU(2) Representations (cont.) Unlimited
  • Lecture 39 – Representation on Function Spaces Unlimited
  • Lecture 40 – Representation on Function Spaces (cont.) Unlimited
  • Lecture 41 – Lorentz Boosts, SO(3,1) Algebra Unlimited
  • Lecture 42 – Lorentz Boosts, SO(3,1) Algebra (cont.) Unlimited
  • Lecture 43 – Representation of Lorentz Group and Clifford Algebra Unlimited
  • Lecture 44 – Representation of Lorentz Group and Clifford Algebra (cont.) Unlimited
  • Lecture 45 – SU (3) and Lie’s Classification Unlimited
  • Lecture 46 – SU (3) and Lie’s Classification: SU(3) Irreducible Unlimited
  • Lecture 47 – Fundamental Symmetries of Physics Unlimited
  • Lecture 48 – Fundamental Symmetries of Physics (cont.) Unlimited

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