A vacuum with double structure

For the purpose of proving the conservation of norm in the field theory of complex mass proposed by one of the present authors, a new space is introduced where the state vectors have a double structure and the norms are complex numbers in general. The new space contains the Hilbert space as a subspace where the norms are real and positive. It is shown that the S-matrix transforms a vector of the Hilbert space into a vector of the same space. Other states in the new space may appear as intermediate virtual states. In this way the field theory of complex mass is formally proved to be physically interpretable. (auth.)