Dr Costis Papageorgakis Project Abstract

Dr Costis Papageorgakis

3rd Year Project Abstract

Topological Solitons

The aim of this project is to study 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 and applications. The role of solitons in Quantum Field Theory will also be investigated.

Pre-requisites: Physical Dynamics, Mathematical Techniques 3

4th Year Project Abstract

Topics in Topological Soliton Quantisation

The 70's brought about a mini-revolution in our understanding of Quantum Field Theory (QFT): The spectrum of many different theories was shown to possess special "heavy" states, broadly called solitons, which are not visible through ordinary perturbation theory around the vacuum but are nevertheless very important for the dynamics at strong coupling. This project will first involve studying solitons as classical solutions in various dimensions and understanding their intricate relation to topology. The concept of a "space of solutions" (module space) will be introduced and its geometric nature emphasised. Finally, the machinery of Quantum Field Theory will be extended to soliton sectors, both in the diagrammatic expansion approach and the path-integral formulation. Upon completion, the student will have accumulated a solid understanding of QFT techniques, appreciated the interplay between topology, geometry and (non-gravitational) field theories and learnt the fundamentals of solitons, which are staple objects in all aspects of modern theoretical physics.

Pre-requisites: Mathematical Techniques 4, Spacetime and Gravity

Juno Champion

The school holds Juno Champion status, the highest award of this IoP scheme to recognise and reward departments that can demonstrate they have taken action to address the under-representation of women in university physics and to encourage better practice for both women and men.