Anatomy of Isolated Monopole in Abelian Projection of SU (2) Lattice Gauge Theory

We study the structure of the isolated static monopoles in the maximal Abelian projection of SU(2) lattice gluodynamics. Our estimation of the monopole radius is: R ≈ 0.06 fm. 1. The monopole confinement mechanism in SU(2) lattice gauge theory is confirmed by many numerical calculations (see e.g. reviews [1]). In the maximal Abelian projection monopole currents form one big cluster and several small clusters. The big cluster, infrared (IR) cluster, percolates and has a nontrivial fractal dimension, Df > 1 [2]. The properties of small, ultraviolet (UV), clusters differs much from those of the IR cluster, it can be shown that the IR monopole cluster is responsible for the confinement of quarks [3]. As it was shown in the recent publication [4] the structure of IR and UV monopoles is completely different, and monopoles in IR clusters are condensed due to their special anatomy. In this publication we study the structure of Abelian monopoles in SU(2) lattice gauge theory in a different way than it was done in ref. [4]. We study the structure of the isolated monopoles, the results show that nontrivial monopole anatomy plays crucial role in the confinement phenomenon. 2. The plaquette action of the compact electrodynamics (cQED), S cQED = βU(1) cos θP , (1) is close to the action of SU(2) lattice gauge theory in the maximal Abelian projection at small values of the bare charge g (in the continuum limit of gluodynamics). The proof is as follows. By definition the maximal Abelian projection corresponds to the maximization of the functional R with respect to all gauge transformations Ω: max Ω R[U l ], U Ω l = Ω UlΩ, R[Ul] = ∑ l Tr[σ3U + l σ3Ul] = ∑