Description

As in many other theories it is possible to perform perturbative calculations within this theory. However, it turns out that protons and their properties cannot be studied in such a way; hence other approaches must be attempted.

One of such approaches is based on a suggestion of Witten that protons can be thought of as soliton solutions of a particular Skyrme model, which, one hopes, provides a non-perturbative description of some bound states in Quantum Chromodynamics.

The project will look at various properties of topological solitons - with most emphasis being placed on their applications to the Skyrme model. We shall not assume any detailed knowledge of particle physics as the emphasis will be on the mathematics of the model and its properties.

At this stage the project can go in one of many directions:

• more physical - looking at various properties of the proton itself;
• more mathematical - looking at other topological models and comparing their properties;
• more numerical - calculating some properties of similar solitons - in lower dimensions;
• more purely mathematical - introducing the rational map ansatz and studing multibaryon field configurations in terms of this ansatz.

Prerequisites

Resources