Nonlinear Schrödinger equations from prequantum classical statistical field theory

Abstract

We derive some important features of the standard quantum mechanics from a certain classical-like model—prequantum classical statistical field theory, PCSFT. In this approach correspondence between classical and quantum quantities is established through asymptotic expansions. PCSFT induces not only linear Schrödinger's equation, but also its nonlinear generalizations. This coupling with “nonlinear wave mechanics” is used to evaluate the small parameter of PCSFT.