Group Theory Methods in Physics

Group Theory Methods in Physics. Instructor: Prof. P. Ramadevi, Department of Physics, IIT Bombay. This course is a first course pitched at UG level so that the students can appreciate the wide applications of the group theory tools in other areas of Physics. Topics covered in this course include: introduction to discrete groups, subgroups and generators, conjugacy classes, symmetric groups, permutation group, cycle notation, direct product groups, semi-direct product groups, symmetries of molecules, point groups and stereographic projection, matrix representation of groups, Reducible and irreducible representation, great orthogonality theorem and character tables, Mulliken notation, tensor product, projection operator, observables, selection rules, Molecular vibrations, continuous groups, Lorentz transformations, orthogonal groups and Lie algebra, Wigner-Eckart theorem, hydrogen atom, and dynamical symmetry. (from

Lecture 09 - Cycle Structure (cont.)

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Lecture 01 - Introduction I
Lecture 02 - Introduction II
Lecture 03 - Normal Subgroup, Coset, Conjugate Group
Lecture 04 - Factor Group, Homomorphism, Isomorphism
Lecture 05 - Factor Group, Homomorphism, Isomorphism (cont.)
Lecture 06 - Conjugacy Classes
Lecture 07 - Permutation Groups
Lecture 08 - Cycle Structure
Lecture 09 - Cycle Structure (cont.)
Lecture 10 - Young Diagram and Molecular Symmetry
Lecture 11 - Point Groups
Lecture 12 - Symmetries of Molecules, Schoenflies Notation
Lecture 13 - Symmetries of Molecules, Stereographic Projection
Lecture 14 - Examples of Molecular Symmetries and Proof Cayley Theorem
Lecture 15 - Matrix Representation of Groups I
Lecture 16 - Matrix Representation of Groups II
Lecture 17 - Reducible and Irreducible Representation I
Lecture 18 - Reducible and Irreducible Representation II
Lecture 19 - Great Orthogonality Theorem and Character Table I
Lecture 20 - Great Orthogonality Theorem and Character Table II
Lecture 21 - Mulliken Notation, Character Table and Basis
Lecture 22 - Tensor Product of Representation
Lecture 23 - Tensor Product and Projection Operator I
Lecture 24 - Tensor Product and Projection Operator II
Lecture 25 - Tensor Product and Projection Operator with an Example
Lecture 26 - Binary Basis and Observables
Lecture 27 - Selection Rules
Lecture 28 - Selection Rules and Molecular Vibrations
Lecture 29 - Molecular Vibration Normal Modes: Classical Mechanics Approach
Lecture 30 - Molecular Vibration Normal Modes: Group Theory Approach
Lecture 31 - Molecular Vibration Modes using Projection Operator
Lecture 32 - Vibrational Representation of Character
Lecture 33 - Infrared Spectra and Raman Spectra
Lecture 34 - Introduction to Continuous Group
Lecture 35 - Generators of Translational and Rotational Transformation
Lecture 36 - Generators of Lorentz Transformation
Lecture 37 - Introduction to O(3) and SO(3) Group
Lecture 38 - SO(n) and Lorentz Group
Lecture 39 - Generalised Orthogonal Group and Lie Algebra
Lecture 40 - Subalgebra of Lie Algebra
Lecture 41 - gl(2,C) and sl(2,C) Group
Lecture 42 - U(n) and SU(n) Group
Lecture 43 - Symplectic Group
Lecture 44 - SU(2) and SU(3) Groups
Lecture 45 - Rank, Weight and Weight Vector
Lecture 46 - Weight Vector, Root Vector, Comparison between SU(2) and SU(3) Algebra
Lecture 47 - Root Diagram, Simple Roots, Adjoint Representation
Lecture 48 - SU(2) Subalgebra, Dynkin Diagrams
Lecture 49 - Fundamental Weights, Young Diagrams, Dimension of Irreducible Representation
Lecture 50 - Young Diagrams and Tensor Products
Lecture 51 - Tensor Product, Wigner-Eckart Theorem
Lecture 52 - Tensor Product of Irreducible Representation 1: Composite Objects from Fundamental Particles
Lecture 53 - Tensor Product of Irreducible Representation 2: Decimet and Octet Diagrams in the Quark Model
Lecture 54 - Clebsch-Gordan Coefficients
Lecture 55 - Quadrupole Moment Tensor (Wigner-Eckart Theorem), Decimet Baryon Wave Function
Lecture 56 - Higher Dimensional Multiplets in the Quark Model
Lecture 57 - Symmetry Breaking in Continuous Groups
Lecture 58 - Dynamical Symmetry in Hydrogen Atom: SO(4) Algebra
Lecture 59 - Hydrogen Atom Energy Spectrum and Degeneracy using Runge-Lenz Vector