RANDOM HILBERT SPACE AND WIENER’S INTERPRETATION OF QUANTUM MECHANICS

Abstract

The special representation of quantum mechanics suggested by Wiener is studied, the wave function being considered as Gaussian random variable, i. e. the vector of the random Hilbert space. The connection between this representation and the well-known Einstein’s program aiming at creating the consistent field formulation of particle physics is revealed, with particles being represented as solitons, clots of some material field satisfying nonlinear equations.