Browse Hierarchy SPA7027P: Differential Geometry in Theoretical Physics

The aim of this course is to complement the core Relativistic Waves and Quantum Fields (RWQF) module by providing the student with some advanced tools essential for research in modern Theoretical Physics. Using the same starting point as RWQF, Maxwell's theory of electromagnetism, we will focus on the Lagrangian formulation of the two most prominent theories of our time: Yang-Mills (gauge) theory and gravity. The alternative notation of differential forms will be explored and the geometric aspects of gauge theory emphasised. Building on this, and introducing elements from group theory and fibre bundles we will introduce classical solitons as localised, finite energy solutions to the classical field equations in various dimensions (kinks in 2d, vortices in 3d, monopoles in 4d, instantons in Euclidean 4d) and discuss their properties, including the existence of zero-modes, associated collective coordinates and moduli spaces.