Soliton-fermion systems and stabilised vortex loops

In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories \cite{Hooft1974} \cite{Polyakov1974} or the skyrme model of hadrons have been proposed as possible non-perturbative bound states which remain stable due to topological quantum numbers. Furthermore when fermions are introduced, under certain conditions one obtains zero-energy solutions \cite{Vega1978}\cite{Jackiw1981} for the Dirac equations localised on the soliton. An implication of such zero-modes is induced fermion number \cite{Jackiw1977} carried by the soliton.