  The method of reduction of a non-Abelian gauge theory to the corresponding
unconstrained system is exemplified for SU(2) Yang-Mills field theory. The
reduced Hamiltonian which describes the dynamics of the gauge invariant
variables is presented in the form of a strong coupling expansion. The physical
variables are separated into fields, which are scalars under spatial rotations,
and rotational degrees of freedom. It is shown how in the infrared limit an
effective nonlinear sigma model type Lagrangian can be derived which out of the
six physical fields involves only one of three scalar fields and two rotational
fields summarized in a unit vector. Its possible relation to the effective
Lagrangian proposed recently by Faddeev and Niemi is discussed.
