Precanonical quantization and the Schrodinger wave functional

A relation between the Schrodinger wave functional and the Clifford-valued wave function which appears in what we call precanonical quantization of fi elds and fulfills a Dirac-like generalized covariant Schrodinger equation o n the space of field and space-time variables is discussed. The Schrodinger wave functional is argued to be the trace of the positive frequency part o f the continual product over all spatial points of the values of the aforem entioned wave function restricted to a Cauchy surface. The standard functio nal differential Schrodinger equation is derived as a consequence of the Di rac-like covariant Schrodinger equation. (C) 2001 Elsevier Science B.V. All rights reserved.