Condensed Matter Physics, 2013, vol. 16, No. 2, 23702:1-13
DOI:10.5488/CMP.16.23702           arXiv:1307.3867

Title: A current algebra approach to the equilibrium classical statistical mechanics and its applications
  N. Bogolubov (The V.A. Steklov Mathematical Institute of RAN, Moscow, Russian Federation)
  A. Prykarpatsky (AGH University of Science and Technology, Krakow, 30-059, Poland; The Ivan Franko State Pedagogical University, Drohobych, Ukraine)

The non-relativistic current algebra approach is analyzed subject to its application to studying the distribution functions of many-particle systems at the temperature equilibrium and their stability properties. We show that the classical Bogolubov generating functional method is a very effective tool for constructing the irreducible current algebra representations and the corresponding different generalized measure expansions including collective variables transform. The effective Hamiltonian operator construction and its spectrum peculiarities subject to the stability of equilibrium many-particle systems are discussed.

Key words: current algebra, Bogolubov generating functional, collective variables representation, Hamiltonian operator reconstruction
PACS: 73.21.Fg, 73.63.Hs, 78.67.De

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