  In the Abelian projection the Yang--Mills theory contains Abelian gauge
fields (diagonal degrees of freedom) and the Abelian matter fields
(off-diagonal degrees) described by a complicated action. The matter fields are
essential for the breaking of the adjoint string. We obtain numerically the
effective action of the Abelian gauge and the Abelian matter fields in quenched
SU(2) QCD and show that the Abelian matter fields provide an essential
contribution to the total action even in the infrared region. We also observe
the breaking of an Abelian analog of the adjoint string using Abelian
operators. We show that the adjoint string tension is dominated by the Abelian
and the monopole contributions similarly to the case of the fundamental
particles. We conclude that the adjoint string breaking can successfully be
described in the Abelian projection formalism.
