  After fixing the Maximal Abelian gauge in SU(2) lattice gauge theory we
decompose the nonabelian gauge field into the so called monopole field and the
modified nonabelian field with monopoles removed. We then calculate respective
static potentials and find that the potential due to the modified nonabelian
field is nonconfining while, as is well known, the monopole field potential is
linear. Furthermore, we show that the sum of these potentials approximates the
nonabelian static potential with 5% or higher precision at all distances
considered. We conclude that at large distances the monopole field potential
describes the classical energy of the hadronic string while the modified
nonabelian field potential describes the string fluctuations. Similar
decomposition was observed to work for the adjoint static potential. A check
was also made of the center projection in the direct center gauge. Two static
potentials, determined by projected $Z_2$ and by modified nonabelian field
without $Z_2$ component were calculated. It was found that their sum is a
substantially worse approximation of the SU(2) static potential than that found
in the monopole case. It is further demonstrated that similar decomposition can
be made for the flux tube action/energy density.
