# InfoCoBuild

## Selected Topics in Mathematical Physics

Selected Topics in Mathematical Physics. Instructor: Professor V. Balakrishnan, Department of Physics, IIT Madras. A basic course in mathematical methods used in physics. Analytic functions of a complex variable. Calculus of residues, Linear response; dispersion relations. Analytic continuation and the gamma function. Mobius transformations. Multivalued functions; integral representations. Laplace transforms. Fourier transforms. Fundamental Green function for the Laplacian operator. The diffusion equation. Green function for the Helmholtz operator; nonrelativistic scattering. The wave equation. The rotation group and all that. (from nptel.ac.in)

 Lecture 36 - The Rotation Group and All That (Part III)

2-to-1 homomorphism between SU(2) and SO(3). The parameter spaces of SU(2) and SO(3). Double connectivity of SO(3). The universal covering group of a Lie group. The group SO(2) and its covering group. The groups SO(n) and Spin (n). Tensor and spinor representations. Parameter spaces of U(n) and SU(n). A bit about the fundamental group (first homotopy group) of a space. Examples.

Go to the Course Home or watch other lectures:

 Lecture 01 - Analytic Functions of a Complex Variable (Part I) Lecture 02 - Analytic Functions of a Complex Variable (Part II) Lecture 03 - Calculus of Residues (Part I) Lecture 04 - Calculus of Residues (Part II) Lecture 05 - Calculus of Residues (Part III) Lecture 06 - Calculus of Residues (Part IV) Lecture 07 - Linear Response; Dispersion Relations (Part I) Lecture 08 - Linear Response; Dispersion Relations (Part II) Lecture 09 - Analytic Continuation and the Gamma Function (Part I) Lecture 10 - Analytic Continuation and the Gamma Function (Part II) Lecture 11 - Mobius Transformations (Part I) Lecture 12 - Mobius Transformations (Part II) Lecture 13 - Mobius Transformations (Part III) Lecture 14 - Multivalued Functions; Integral Representations (Part I) Lecture 15 - Multivalued Functions; Integral Representations (Part II) Lecture 16 - Multivalued Functions; Integral Representations (Part III) Lecture 17 - Multivalued Functions; Integral Representations (Part IV) Lecture 18 - Laplace Transforms (Part I) Lecture 19 - Laplace Transforms (Part II) Lecture 20 - Fourier Transforms (Part I) Lecture 21 - Fourier Transforms (Part II) Lecture 22 - Fourier Transforms (Part III) Lecture 23 - Fundamental Green Function for Δ2 (Part I) Lecture 24 - Fundamental Green Function for Δ2 (Part II) Lecture 25 - The Diffusion Equation (Part I) Lecture 26 - The Diffusion Equation (Part II) Lecture 27 - The Diffusion Equation (Part III) Lecture 28 - The Diffusion Equation (Part IV) Lecture 29 - Green function for (Δ2 + k2); Nonrelativistic Scattering (Part I) Lecture 30 - Green function for (Δ2 + k2); Nonrelativistic Scattering (Part II) Lecture 31 - Green function for (Δ2 + k2); Nonrelativistic Scattering (Part III) Lecture 32 - The Wave Equation (Part I) Lecture 33 - The Wave Equation (Part II) Lecture 34 - The Rotation Group and All That (Part I) Lecture 35 - The Rotation Group and All That (Part II) Lecture 36 - The Rotation Group and All That (Part III)