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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 43 - Representation of Lorentz Group and Clifford Algebra

In this lecture, the SO(3,1) Algebra and its Physical Application will be introduced to the students.


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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.)