On the precanonical structure of the Schrödinger wave functional in curved space-time

The functional Schrödinger equation in curved space-time is derived from the manifestly covariant precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional product integral of precanonical wave function restricted to a field configuration. The functional Schrödinger representation of QFT in curved space-time appears as a singular limiting case of a formulation based on precanonical quantization, which leads to a hypercomplex generalization of quantum formalism in field theory.