Solitons in High Energy Physics

Abstract: Solitons are solutions to classical field equations that are particle like, meaning they are localized in space, have definite energy and can be stable against deformations into the vacuum. In this thesis we investigate under which circumstances such solutions may exist and what effects their existence could have. It will turn out that topological considerations will play a large role in the question of existence and stability, and that results depend on the number of spatial dimensions in which the theory is defined. Mixed in with the more general results are several examples of solitons, like sine-Gordon kinks, vortices and magnetic monopoles, that serve the purpose of illustrating the ideas behind the arguments as well as showing what effects the existence of solitons may have. A large part of the thesis is dedicated to showing the equivalence of the sine-Gordon model and the massive Thirring model. The equivalence of the two theories will make it possible to connect the strong coupling regime of one theory to the weak coupling regime of the other, and vice versa. It will also be possible to connect the fermion number of the Thirring model to the topological charge of the sine-Gordon model.