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Renormalizability of the time-dependent variational equations in quantum field theory.

The field-theoretic time-dependent variational approximation allows the study of dynamics by a formalism which reflects some of the nonlinearities of the full theory. We study renormalizability of the time-dependent variational equations which are obtained when a Gaussian trial wave functional is used. Renormalizability depends on the specified initial data. We develop reasonable criteria for limiting the initial data, and show that the time-dependent variational equations are made finite by the renormalization prescription used in the vacuum sector.