Noncritical Virasoro algebra of the d<1 matrix model and the quantized string field

On the basis of the second quantized operator formalism of the one-matrix model of a non-perturbative string, we construct a noncritical Virasoro algebra representing the diffeomorphism of an eigenvalue coordinate. It is shown to be the origin of the formal Virasoro conditions, which we find are not limited to the double scaling limit. Also discussed are an interpretation of the formalism as a string field theory, the transmutation of the eigenvalue coordinate into an embedding dimension, the operator product of string fields, and a determinant formula for the partition function driven by a set of scaling operators. (orig.)