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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 nptel.ac.in)

Lecture 30 - Molecular Vibration Normal Modes: Group Theory Approach

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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