, Volume 9, Issue 4, pp 293-302

Quasi-free states of the C.C.R.—Algebra and Bogoliubov transformations

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We give a complete characterization of quasi-free states (generalized free states) of the C.C.R. algebra. We prove that the pure quasi-free states areall Fock states and that any two Fock states are related through a symplectic automorphism (Bogoliubov transformation). We make an explicit construction of these representations which correspond to primary quasi-free states.

Work under contract D.G.R.S.T.
Attaché de Recherches au C.N.R.S. This work is part of a “Thèse de Doctorat d'Etat” presented to the “Faculté des Sciences de Marseille” in May 1968, under the number A.O.2.323.
Aangesteld Navorser van het Belgisch N.F.W.O. On leave from University of Louvain (Belgium).