2 Vortices

We are now going to start studying vortices. These are topological solitons in

two space dimensions. While we mostly studied

φ

4

kinks last time, what we are

going to do here is more similar to the sine-Gordon theory than the

φ

4

theory,

as it is largely topological in nature.

A lot of the computations we perform in the section are much cleaner when

presented using the language of differential forms. However, we shall try our

best to provide alternative versions in coordinates for the easily terrified.