Topological Quantization of Instantons in SU(2) Yang--Mills Theory

By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang--Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin
defects in the non-trivial sector of Yang--Mills theory.