Abelian Monopoles in $\mathrm{SU}\left(2\right)$ Lattice Gauge Theory as Physical Objects

By numerical calculations we show that the Abelian monopole currents are locally correlated with the density of the $\mathrm{SU}\left(2\right)$ lattice action. This fact is established for the maximal Abelian projection. Thus, in the maximal Abelian projection, the monopoles are physical objects; they carry the $\mathrm{SU}\left(2\right)$ action. Calculations on the asymmetric lattice show that the correlation between monopole currents and the density of the $\mathrm{SU}\left(2\right)$ lattice action also exists in the deconfinement phase of gluodynamics.