  We reexamine in detail a canonical quantization method a la Gupta-Bleuler in
which the Fock space is built over a so-called Krein space. This method has
already been successfully applied to the massless minimally coupled scalar
field in de Sitter spacetime for which it preserves covariance. Here, it is
formulated in a more general context. An interesting feature of the theory is
that, although the field is obtained by canonical quantization, it is
independent of Bogoliubov transformations. Moreover no infinite term appears in
the computation of $T^{\mu\nu}$ mean values and the vacuum energy of the free
field vanishes: $<0|T^{00}|0>=0$. We also investigate the behaviour of the
Krein quantization in Minkowski space for a theory with interaction. We show
that one can recover the usual theory with the exception that the vacuum energy
of the free theory is zero.
