03-27 Sergej A. Choroszavin ( [email protected] )

Among Quadratic Hamiltonians, Bogoliubov Transformations and Non-Regular States on CCRs *-Algebra. I. Pure and Invariant States. (In the Mood for the Manuceau Verbeure Theorems about Quasi-free States and Automorphisma of the CCR Algebra) (85K, LaTeX 2.09) Jan 20, 03

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Abstract. The features of the paper are these: 1) we discuss {\bf especially } quadratic (alias bilinear) Bose-Hamiltonians, the related Bogoliubov transformations and {\bf especially } quasi-free-like (alias coherent or Fock-like) states 2) we discuss {\bf any } quadratic Bose-Hamiltonians and Bogoliubov transformations, whether diagonalizable or not, whether proper or improper, and {\bf arbitrary } quasi-free-like states, whether regular or non-regular they are 3) we associate notions and terms of the CCRs theory \footnote{ CCRs = Canonical Commutation Relations } with notions and terms of the indefinite inner product spaces theory. Then, we apply the corresponding `bilingual dictionary' so as to construct invariant states of some of the quadratic Hamiltonians.

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