Abstract
The author constructs the Schrödinger representation in the quantum theory of fields, strings, and membranes on a mathematical level of rigor. This representation is based on the theory of pseudodifferential operators on an infinite-dimensional superspace, developed by the author within the framework of functional superanalysis. In the Schrödinger representation, the author realizes all the basic operators of quantum mechanics with fermion-boson coordinates, the operators of quantum field theory (including supersymmetric field theory), and the operators of the quantum and field theory of strings and membranes (Hamiltonians of fields with polynomial self-action in a space of arbitrary dimension. Virasoro operators, the BRST charge operator which forms the basis of boson string gauge theory, the gauge-invariant Hamiltonian of a boson string, and the Hamiltonian of a supermembrane). It should be noted that the representation constructed here does not satisfy the canonical axiomatics of quantum theory — the state space is not Hilbert space. Bibliography: 45 titles.