A self-dual CCR algebra is defined and arbitrary quasifree state is realized in a Fock type representation of another self-dual CCR algebra of a double size as a preparation for a study of quasi-equivalence of quasifree states. § 1. Introduction A necessary and sufficient condition for the quasi-equivalence of two quasifree representations of the canonical anticommutation relations (CAR) has been derived in [11] for the gauge invariant case and in [3] for the general case. We shall derive an analogous result for the canonical commutation relations (CCR) In section 2, we review the formulation in [2]. A self-dual algebra is defined when a linear space K, an antilinear involution F of K and a hermitian form j" on K satisfying f(Tf^ Fg) = -/(/i #)* are given. In section 3, we define a quasifree state in terms of a nonnegative hermitian form S on K such that S(f, g)-S(r g , r/) = r(/, g). In section 4, the structure of S relative to (K, 7% /") is analyzed. In section 5, basic properties of a Fock representation are stated and a result in [1] is quoted. A Fock type representation is defined as a generalization of a Fock representation to the case of degenerate 7* (i.e.

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We have already reported the in vitro effect of the ultrasound wave stimulation for the hydroxyapatite-like crystalline formation on bioactive pure titanium surface in previous study ( Part I )

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