Structure of Multi-Meron Knot Action

We consider the structure of multi-meron knot action in the Yang-Mills theory and in the CP¹ Ginzburg-Landau (GL) model. Self-dual equations have been obtained without identifying orientations in the space-time and in the color space. The dependence of the energy bounds on topological parameters of coherent states in planar systems is also discussed. In particular, it is shown that a characteristic size of a knot in the Faddeev-Niemi model is determined by the Hopf invariant.