PH4990 Advanced Theoretical Physics

A graduate-level introduction to the methods of theoretical physics. Beginning with complex variable methods as a tool for solving problems in physics, the Kramers-Kronig formulas are derived (connection between analyticity and causality in stable physical systems), together with the Hilbert transform and its role in defining the analytic signal and the extension of phasors to time-varying systems. The stationary phase approximation is derived as a method of treating the high-frequency behavior of oscillatory integrals, important for wave transmission and scattering.The method of Green functions for solving inhomogeneous differential equations is developed, with applications of Green functions as propagators affecting the response of physical systems to the influence of sources. An introduction to integral equations provides the foundation for scattering problems in physics, both electromagnetic and quantum. The essentials of tensor calculus aredeveloped, the language of the general theory of relativity (necessary for understanding the Global Positioning System and other physical systems) and of physical processes in anisotropic media.

Prerequisite

PH3991 or equivalent coverage of partial differential equations, special functions, and Fourier analysis.

Lecture Hours

4

Lab Hours

0