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 {\it nonlinear generalizations.} This coupling with ``nonlinear wave mechanics'' is used to evaluate the small parameter of PCSFT.

Links to theory of nonlinear Schrodinger equation; new model of physical space: Infinite-Dimensional Physical Space

References in corpus (3)

• Prequantum classical statistical model with infinite dimensional phase-space
• A succinct presentation of the quantized Klein-Gordon field, and a similar quantum presentation of the classical Klein-Gordon random field
• A relativistic variant of the Wigner function

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