THEORETICAL PHYSICS (Part 1)

E M Terentjev and C H W Barnes

Revision of Lagrangian mechanics: General coordinate systems, constraints. Principle of the least action. Canonical momenta. Symmetries and conservation laws.

Hamilton’s equations: Variational principles. Poisson brackets and the transition to quantum mechanics. Liouville’s Theorem. Velocity-dependent potentials; charged particle in electromagnetic field.

Relativistic Lagrangian dynamics: Revision of 4-index notation. Relativistic particle in electromagnetic and gravitation fields.

Continuum Field Theory: Lagrangian formulation of scalar field theory. Canonical momentum density and the current. Vector and tensor field theory: elasticity, electromagnetic field; gravity as a Lagrangian field theory.

Rayleigh Dissipation Function: Generalised friction. Fundamentals of fluid dynamics.

Linear response and propagators: Spectral (Fourier) analysis. Integration on the complex plane and causality. Kramers-Kronig relations.

Elements of Stochastic Physics: Brownian motion via the Langevin equation and the probability distribution. Fluctuation-dissipation theorem, once again. Gaussian processes and diffusion. Fokker-Planck equation.

Introduction to Path Integrals: Path integral formulation of classical diffusion. Lead on to Feynman path-integral formulation of quantum mechanics.

The course is discontinued as a Part II Theoretical Option. This website is all that's left if you want to use it as reference material, with no handout and no liability accepted ...