Gauge Structures of SU(3) Skyrme Model, and Construction of SU(3) Generators Including Induced Gauge Field

Abstract

The SU(3) Skyrme–Witten baryon model with the embedded SU(2) soliton solution, the quantum mechanical aspect of which has been examined in the eighth decade, is reconsidered from the viewpoint of the gauge structure induced on a curved manifold. By construction, we have to consider the quantum mechanics on the coset space SU(3)/U(1), The expected U(1) gauge field comes from Wess–Zumino–Witten term in the field theory of the SU (3) nonlinear σ model, and geometrical properties of the gauge field are fully examined. The SU(3) generators including the gauge field, given in the preceding paper, are shown to coincide with those constructed along a way similar to the SU(2)/U(1) case in accordance with Biedenharn’s suggestion. Some concrete forms of the gauge field expressed in an eight-dimensional Euclidean space E 8 are given, the first of three components of which are the known gauge fields of a magnetic monopole in E 3 with Dirac and Schwinger string singularities. The described prescriptions and procedures are pointed out to be commonly applicable to the coset SU(n)/U(1) case with n ≥ 2, in which some induced gauge field generally exists.