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.
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