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Theoretical and mathematical physics

Non-Fock Representations

Franco Strocchi

Published Jan 1, 2021• 0 citations
Publisher

Abstract

As anticipated in the previous discussions, the Fock representation is very special to the finite-dimensional case and to free fields. Actually, as a consequence of Proposition 12.1 , non-Fock representationsNon-Fock representation are required in order to describe many-particle systems with non-zero density in the thermodynamical limit.
DOI
10.1007/978-3-662-62166-0_13

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This paper is a study of the representations of the current algebra for an infinite, free, Bose or Fermi system at finite temperature. The state of the algebra is calculated for a finite system by use of the grand canonical formalism of statistical physics, and the thermodynamic limit is used to get the representation of the infinite case. An expression of the states is given in terms of determinants of one particle operators. In a second part, the usual formulas for the occupation density, the condensation temperature for bosons, etc., are recovered. It is also found that the canonical and grand canonical formalisms are equivalent when used to study Fermi systems in the thermodynamic limit, but not so for the Bose systems. It is postulated that this has something to do with the phase transition of Bose systems. Finally, the problem of the Hamiltonian is discussed in some details. The states calculated previously are used to test a method for calculating expectation values of the Hamiltonian, given the states of the algebra; it yields the correct value for the case of the free system at finite temperature.