The instanton configuration in the SU(2)-gauge system with a Higgs doublet is constructed by using the new valley method. This method defines the configuration by an extension of the field equation and allows the exact conversion of the quasi-zero eigen-mode to a collective coordinate. It does not require ad hoc constraints used in the current constrained instanton method and provides a better mathematical formalism than the constrained instanton method. The resulting instanton, which we call “valley instanton”, is shown to have the desirable behaviors. The result of the numerical investigation is also presented.
Collective coordinate quantization and spin statistics of the solitons in theCPNSkyrme-Faddeev model