  For a high temperature non-Abelian plasma, we reformulate the hard thermal
loop approximation as an effective classical thermal field theory for the soft
modes. The effective theory is written in local Hamiltonian form, and the
thermal partition function is explicitly constructed. It involves an
ultraviolet cutoff which separates between hard and soft degrees of freedom in
a gauge-invariant way, together with counterterms which cancel the cutoff
dependence in the soft correlation functions. The effective theory is well
suited for numerical studies of the non-perturbative dynamics in real time, in
particular, for the computation of the baryon number violation rate at high
temperature.
