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Classical pure states: Information and symmetry in statistical mechanics

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Abstract

The aim of this paper is to find classical counterparts of pure quantum states. It is shown that these are singular probability distributions concentrated on the so-called maximal null manifolds in a phase space. They are equivalent to densities studied by Van Vleck and Schiller and to WKB solutions (cf. Van Vleck, 1928; Schiller, 1962). Properties of such distributions and their relativistic generalisations have been studied in previous papers (Sławianowski, 1971; Slawianowski, 1972). However, it has not been shown there that such distributions arise actually in the limith→0. When working with the standard apparatus of differential geometry we mostly use the language of Kobayashi & Nomizu (1963).

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Authors and Affiliations

  1. Department of the Theory of Continuous Media, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw

    Jan J. Sławianowski

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  1. Jan J. Sławianowski
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Sławianowski, J.J. Classical pure states: Information and symmetry in statistical mechanics. Int J Theor Phys 8, 451–462 (1973). https://doi.org/10.1007/BF00670979

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