On field theory quantization around instantons

Various aspects of the so-called topological embedding, a procedure recently proposed for quantizing a field theory around a non-discrete space of classical minima, are discussed and collected in a simple logical scheme. The possible physical implications are pointed out. The compatibility of the procedure with renormalization is illustrated in the case of the Yang-Mills theory expanded around instantons. The quantum topological properties of Yang-Mills instantons are re-derived in a simpler and illustrative way. Moreover, the general approach is applied to the free energy of the Ginzburg-Landau theory of superconductivity in the intermediate situation between type I and type II superconductors. The topological version of the theory is solved and the quantum topological sectors of the static vortices are classified.