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We use our previous idea, in which at first we perform a naive secondquantization of both negative and positive energy for the Klein-Gordon equationanalogous to the unfilled Dirac sea for fermions, to study as a playground thisnaive second quantization theory. It is not to be taken seriously physically inas far as it has indefinite Fock space, but it has nevertheless interestingpossibilities: Although the naive (quantization) theory represents aspontaneous breakdown of the usual CPT-symmetry, we shall show that it obeys acertain replacement for the CPT-theorem for which a proof is presented indetail.Comment: 20 pages, no figure, LaTeX; added refereces, corrected typo

Dirac Sea for Bosons. II: -- Study of the Naive Vacuum Theory for the Toy Model World Prior to Filling the Negative Energy Sea --