Fermionic Meixner classes, Lie algebras and quadratic Hamiltonians

L. Accardi, I. Ya. Aref’eva () and I. V. Volovich ()
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L. Accardi: Università di Roma “Tor Vergata”
I. Ya. Aref’eva: Steklov Mathematical Institute
I. V. Volovich: Steklov Mathematical Institute

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 4, 517-538

Abstract: Abstract We introduce the quadratic Fermi algebra, which is a Lie algebra, and calculate the vacuum distributions of the associated Hamiltonians. In order to emphasize the difference with the Bose case, we apply a modification of the method used in the above calculation to obtain a simple and straightforward classification of the 1-dimensional Meixner laws in terms of homogeneous quadratic expressions in the Bose creation and annihilation operators. There is a huge literature of the Meixner laws but this, purely quantum probabilistic, derivation seems to be new. Finally we briefly discuss the possible multidimensional extensions of the above results.

Keywords: Meixner probability distributions; Lie algebra; quantum Fermi and Bose hamiltonians (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0150-7

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