INITIAL CONDITIONS IN QUASI-CLASSICAL FIELD-THEORY

We investigate the problem of divergences and renormalizations in the Hamiltonian formalism of quasiclassical field theory. This approach is known to involve divergences in the leading term of the expansion. Pr oposals have been made to eliminate the divergences by using nonequiva lent representations of the canonical commutation relations at differe nt moments of time. In this paper, we consider the Schrodinger equatio n with ultraviolet and infrared cutoffs. In order to remove the cutoff s, conditions are imposed on the initial state of the regularized theo ry in addition to the conditions imposed on the counterterms in the Ha miltonian. In the leading order of the quasi-classical expansion, we g ive the explicit form of these conditions, which is invariant under th e evolution. This allows us to show that this approximation does not r equire the introduction of nonunitary evolution transformations.