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We first construct a Fock space with an indefinite metric =( , T), where T is a unitary and Hermitian operator. We define a T-selfadjoint (Segal's) field F?(f) which obeys the canonical commutation relations (CCR) with an indefinite metric. We consider a transformation 349-2 (T = real linear) which leaves the CCR invariant. We investigate the implementability of T by an operator on the Fock space.

Canonical linear transformation on Fock space with an indefinite metric