Andrei Khrennikov 2005 J. Phys. A: Math. Gen. 38 9051 doi:10.1088/0305-4470/38/41/015
A pre-quantum classical statistical model with infinite-dimensional phase space
Andrei Khrennikov
Show affiliationsWe study the problem of correspondence between classical and quantum statistical models. We show that (contrary to a rather common opinion) it is possible to construct a natural pre-quantum classical statistical model. The crucial point is that such a pre-quantum classical statistical model is not the conventional classical statistical mechanics on the phase space R2n, but its infinite-dimensional analogue. Here the phase space Ω = H × H, where H is the (real separable) Hilbert space. The classical → quantum correspondence is based on the Taylor expansion of classical physical variables—maps f:Ω → R. The space of classical statistical states consists of Gaussian measures on Ω having zero mean value and dispersion ≈h. The quantum statistical model is obtained as the limh→0 of the classical one. All quantum states including so-called 'pure states' (wavefunctions) are simply Gaussian fluctuations of the 'vacuum field', ω = 0 
Ω, having dispersions of the Planck magnitude.
- PACS
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03.65.Yz Decoherence; open systems; quantum statistical methods
03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
- Subjects
- Dates
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Issue 41 (14 October 2005)
Received 1 June 2005, in final form 31 August 2005
Published 28 September 2005
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A pre-quantum classical statistical model with infinite-dimensional phase space
Andrei Khrennikov 2005 J. Phys. A: Math. Gen. 38 9051
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