Dirac Sea for Bosons II -- Study of the Naive Vacuum Theory for the   Playground World Prior to Filling the Negative Energy Sea --
  We use our previous idea, in which at first we perform a naive second quantization of both negative and positive energy for the Klein-Gordon equation analogous to the unfilled Dirac sea for fermions, to study as a playground this naive second quantization theory. It is not to be taken seriously physically in as far as it has indefinite Fock space, but it has nevertheless interesting possibilities: Although the naive (quantization) theory represents a spontaneous breakdown of the usual CPT-symmetry, we shall show that it obeys a certain replacement for the CPT-theorem for which a proof is presented in detail. 
Holger B. Nielsen and Masao Ninomiya