  Quantum theory of Lorentz invariant local scalar fields without restrictions
on 4-momentum spectrum is considered. The mass spectrum may be both discrete
and continues and the square of mass as well as the energy may be positive or
negative. Such fields can exist as part of a hidden matter in the Universe if
they interact with ordinary fields very weakly. Generalization of
Kallen-Lehmann representation for propagators of these fields is found. The
considered generalized fields may violate CPT- invariance. Restrictions on
mass-spectrum of CPT-violating fields are found. Local fields that annihilate
vacuum state and violate CPT- invariance are constructed in this scope. Correct
local relativistic generalization of Lindblad equation for density matrix is
written for such fields. This generalization is particulary needed to describe
the evolution of quantum system and measurement process in a unique way.
Difficulties arising when the field annihilating the vacuum interacts with
ordinary fields are discussed.
