  A dynamical effective medium theory is presented for quantum spins and higher
multipoles such as quadrupole moments. The theory is a generalization of the
spherical model approximation for the Ising model, and is accurate up to
O(1/z_n) where z_n is the number of interacting neighbors. The polarization
function is optimized under the condition that it be diagonal in site indices.
With use of auxiliary fields and path integrals, the theory is flexibly applied
to quantum spins and higher multipoles with many interacting neighbors. A
Kondo-type screening of each spin is proposed for systems with extreme quantum
fluctuations but without conduction electrons.
