Description

This project is all about the study of solitons in various dimensions and understanding some of their peculiar properties. For example kinks (or domain walls) can be seen as waves travelling without any dissipation. Vortices are responsible for the draining of the water in your sink, and arise in a different guise in superconductors. Monopoles are the objects that you will never obtain by breaking a magnet in two! Between the possible topics:

• Kinks solutions in two-dimensions, fermionic zero-modes and Derrick's theorem.
• The Abrikosov-Nielsen-Olesen vortex, the motion and scattering of vortices.
• The 't Hooft-Polyakov monopole, electro-magnetic duality of the Maxwell equations. Dyonic solutions.

Pre- Co-requisites

2H Mathematical Physics or equivalently Theoretical Physics II. (Lagrangian formulation).

3H Quantum Mechanics or equivalently Foundations of Physics 2A (Not necessary, but it's helpful).

4H Advanced quantum theory IV or equivalently the corresponding module in Physics. (Introduction to quantum fields)

Resources

For some background:

• Have a look at this weirdly fascinating video;
• search for ``Solitons'' on the web.

Reading material.

• Topological solitons, N.Manton and P.Sutcliffe, CUP.
• TASI lectures on solitons: Instantons, monopoles, vortices and kinks, D. Tong, hep-th/0509216 .
• Aspects of symmetry, S. Coleman, CUP.