Sergej A. Choroszavin ( sergius@pve.vsu.ru )
 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)

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.