MAS415   Topics in Mathematical Physics   (15 credits)

Description

This unit will introduce students to advanced concepts and techniques in modern mathematical physics, in preparation for research-level activities. It is assumed that the student comes equipped with a working knowledge of analytical dynamics, and of non-relativistic quantum theory. We will examine how key physical ideas are precisely formulated in the language of mathematics. For example, the idea that fundamental particles arise as excitations of relativistic quantum fields finds its mathematical realisation in Quantum Field Theory. In QFT, particles can be created from the vacuum, and destroyed, but certain other quantities such as charge, energy, and momentum are conserved (after averaging over quantum fluctuations). We will examine links between conservation laws and invariants, and the underlying (discrete or continuous) symmetry groups of theories. We will also develop powerful calculation tools. For example, to find the rate of creation of new particles in a potential, one must evaluate the terms in a perturbative (Feynman-diagram) expansion. For details of the current syllabus, please consult the module leader.

Reading List