Abstract
Reducible quasi-Fock representations of canonical commutation relations (CCR) are studied which result from uninvertible linear canonical transformations of the Fock representation. Necessary and sufficient conditions are proved for: (i) invertibility of the linear canonical transformation, (ii) quasi-Fock character of the obtained representation of CCR, (iii) coincidence of the vacuum subspaces of two representations of this type, (iv) coincidence of W ∗-algebras of operators of these representations. The results obtained are interesting for constructive quantum field theory with asymptotic fields giving rise to the quasi-Fock representations of CCR.
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