Method of asymptotic operators in statistical mechanics

S. V. Peletminskiǐ, V. I. Prikhod'ko

V. A. Krasnikov

Osvaldo Civitarese, Manuel Gadella

Andrei Yu. Khrennikov

We show that quantum mechanics can be represented as an asymptotic projection of statistical mechanics of classical fields. Our approach does not contradict to a rather common opinion that quantum mechanics could not be reduced to statistical mechanics of classical particles. Notions of a system and causality can be reestablished on the prequantum level, but the price is sufficiently high — the infinite dimension of the phase space. In our approach quantum observables, symmetric operators in the Hilbert space, are obtained as the second order derivatives of functionals of classical fields: f(ψ) → Aquant = f″(0). Statistical states are given by Gaussian ensembles of classical fields with zero mean value (so these are vacuum fluctuations) and dispersion α which plays the role of a small parameter of the model (so these are small vacuum fluctuations). Our approach can be called Prequantum Classical Statistical Field Theory — PCSFT.

David A. Lavis, G. M. Bell

N. N. Bogolyubov, J.G. Brankov, Valentin Anatol'evich Zagrebnov +2 more

CONTENTS Introduction ??1. Model systems with positive and negative interaction components ??2. Model systems with non-polynomial interaction ??3. The asymptotic proximity of thermodynamic averages. Quasi-averages ??4. Model systems with interaction containing unbounded operators ??5. Thermodynamic averages and quasi-averages Conclusion References