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Nonlinear Schrödinger equations from prequantum classical statistical field theory

Andrei Khrennikov
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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.

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Andrei Khrennikov. 2006-04-23. Nonlinear Schrödinger equations from prequantum classical statistical field theory. https://doi.org/10.1016/j.physleta.2006.04.046

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