 0327 Sergej A. Choroszavin ( sergius@pve.vsu.ru )
 Among Quadratic Hamiltonians, Bogoliubov Transformations
and NonRegular States on CCRs *Algebra. I. Pure and Invariant States.
(In the Mood for the Manuceau Verbeure Theorems
about Quasifree 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)
BoseHamiltonians, the related Bogoliubov transformations
and {\bf especially } quasifreelike (alias coherent or Focklike) states
2) we discuss {\bf any } quadratic BoseHamiltonians and
Bogoliubov transformations, whether diagonalizable or not,
whether proper or improper, and {\bf arbitrary } quasifreelike states,
whether regular or nonregular 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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