Geodesic
Two-particle wave function as an~integral operator and the~random field approach to quantum correlations
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 386-393

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We propose a new interpretation of the wave function $\Psi(x,y)$ of a two-particle quantum system, interpreting it not as an element of the functional space $L_2$ of square-integrable functions, i.e., as a vector, but as the kernel of an integral (Hilbert–Schmidt) operator. The first part of the paper is devoted to expressing quantum averages including the correlations in two-particle systems using the wave-function operator. This is a new mathematical representation in the framework of conventional quantum mechanics. But the new interpretation of the wave function not only generates a new mathematical formalism for quantum mechanics but also allows going beyond quantum mechanics, i.e., representing quantum correlations (including those in entangled systems) as correlations of (Gaussian) random fields.
Keywords: classical wave, quantum average, wave function, integral operator. 
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     author = {A. Yu. Khrennikov},
     title = {Two-particle wave function as an~integral operator and the~random field approach to quantum correlations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {386--393},
     publisher = {mathdoc},
     volume = {164},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a6/}
}
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A. Yu. Khrennikov. Two-particle wave function as an~integral operator and the~random field approach to quantum correlations. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 386-393. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a6/