The vacuum as an expectation
value form on the Clifford or Weyl algebra over an orthogonal or symplectic real
linear space, invariant under a given group of automorphisms of such, is treated
without assumptions as to self-adjointness or positivity. This is necessary for the
quantization of fields that transform non-unitarily, in particular indecomposably,
such as the full section spaces of typical conformally invariant bundles over
space-times. A stability condition in the nature of positivity of the energy is shown to
be sufficient to characterize the vacuum for the basic case of a one-parameter group.
In application e.g. to spannor fields transforming under SU(2,2), this results in a
vacuum invariant under the maximal subgroup K, giving rise to a natural broken
symmetry.
