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Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 278-291 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that in contrast to a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. We consider an approximation based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the second-order term. To escape technical difficulties related to the infinite dimensionality of the phase space for quantum mechanics, we consider finite-dimensional quantum mechanics. On one hand, this is a simple example with high pedagogical value. On the other hand, quantum information operates in a finite-dimensional state space. Therefore, our investigation can be considered a construction of a classical statistical model for quantum information.
Keywords: quantum average, classical average, approximation, small parameter, Taylor expansion.
Mots-clés : von Neumann trace formula 
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A. Yu. Khrennikov. Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 2, pp. 278-291. http://geodesic.mathdoc.fr/item/TMF_2007_152_2_a5/

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