  A quantum perfect lattice action in four dimensions can be derived
analytically as a renormalized trajectory when we perform a block spin
transformation of monopole currents in a simple but non-trivial case of
quadratic monopole interactions. The spectrum of the lattice theory is
identical to that of the continuum theory. The perfect monopole action is
transformed exactly into a lattice action of a string model. A perfect operator
evaluating a static potential between electric charges is also derived
explicitly. If the monopole interactions are weak as in the case of infrared
SU(2) QCD, the string interactions become strong. The static potential and the
string tension is estimated analytically by the use of the strong coupling
expansion and the continuum rotational invariance is restored completely.
