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Theory of Groups for Physics Applications

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)

Lecture 27 - Classical Groups

In this lecture, the students will be familiarised with the concepts of Matrix Group, Inner product as well as the necessary Cauchy Convergence and Completeness conditions.

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Lecture 01 - Introduction

Lecture 02 - Algebraic Preliminaries

Lecture 03 - Basic Group Concepts and Low Order Groups

Lecture 04 - Basic Group Concepts and Low Order Groups (cont.)

Lecture 05 - Lagrange's Theorem and Cayley's Theorem

Lecture 06 - Lagrange's Theorem and Cayley's Theorem (cont.)

Lecture 07 - Factor Group Conjugacy Classes

Lecture 08 - Factor Group Conjugacy Classes (cont.)

Lecture 09 - Cycle Structures and Molecular Notation

Lecture 10 - Cycle Structures and Molecular Notation (cont.)

Lecture 11 - Cycle Structures and Classification

Lecture 12 - Cycle Structures and Classification (cont.)

Lecture 13 - Point Group Notation and Factor Group

Lecture 14 - Point Group Notation and Factor Group (cont.)

Lecture 15 - Representation Theory I

Lecture 16 - Representation Theory II

Lecture 17 - Representation Theory III

Lecture 18 - Representation Theory IV

Lecture 19 - Schur's Lemma and Orthogonality Theorem

Lecture 20 - Schur's Lemma and Orthogonality Theorem (cont.)

Lecture 21 - Orthogonality for Characters

Lecture 22 - Orthogonality for Characters (cont.)

Lecture 23 - Character Tables and Molecular Applications

Lecture 24 - Character Tables and Molecular Applications (cont.)

Lecture 25 - Preliminaries about the Continuum

Lecture 26 - Preliminaries about the Continuum (cont.)

Lecture 27 - Classical Groups

Lecture 28 - Classical Groups (cont.)

Lecture 29 - Classical Groups - Topology

Lecture 30 - Classical Groups - Topology (cont.)

Lecture 31 - SO(3) and Matrix Exponent

Lecture 32 - SO(3) and Matrix Exponent (cont.)

Lecture 33 - Generators, Discussion of Lie's Theorems

Lecture 34 - Generators, Discussion of Lie's Theorems (cont.)

Lecture 35 - Group Algebras; SO(3)-SU(2) Correspondence

Lecture 36 - Group Algebras; SO(3)-SU(2) Correspondence (cont.)

Lecture 37 - SO(3), SU(2) Representations

Lecture 38 - SO(3), SU(2) Representations (cont.)

Lecture 39 - Representation on Function Spaces

Lecture 40 - Representation on Function Spaces (cont.)

Lecture 41 - Lorentz Boosts, SO(3,1) Algebra

Lecture 42 - Lorentz Boosts, SO(3,1) Algebra (cont.)

Lecture 43 - Representation of Lorentz Group and Clifford Algebra

Lecture 44 - Representation of Lorentz Group and Clifford Algebra (cont.)

Lecture 45 - SU (3) and Lie's Classification

Lecture 46 - SU (3) and Lie's Classification: SU(3) Irreducible

Lecture 47 - Fundamental Symmetries of Physics

Lecture 48 - Fundamental Symmetries of Physics (cont.)