Indian Journal of Pure and Applied Mathematics

, Volume 46, Issue 4, pp 517–538 | Cite as

Fermionic Meixner classes, Lie algebras and quadratic Hamiltonians

  • L. Accardi
  • I. Ya. Aref’evaEmail author
  • I. V. Volovich


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.


Meixner probability distributions Lie algebra quantum Fermi and Bose hamiltonians 


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© The Indian National Science Academy 2015

Authors and Affiliations

  • L. Accardi
    • 1
  • I. Ya. Aref’eva
    • 2
    Email author
  • I. V. Volovich
    • 2
  1. 1.Centro Vito VolterraUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Steklov Mathematical InstituteMoscowRussia

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