  In this paper we consider properties of the space-time manifold M caused by
the proposition that, according to the scheme theory, the manifold M is locally
isomorphic to the spectrum of the algebra A, M = Spec(A), where A is the
commutative algebra of distributions of quantum-field densities. In order to
determine the algebra A, it is necessary to define multiplication on densities
and to eliminate those densities, which cannot be multiplied. This leads to
essential restrictions imposed on densities and on space-time properties. It is
found that the only possible case, when the commutative algebra A exists, is
the case, when the quantum fields are in the spacetime manifold M with the
structure group SO(3,1) (Lorentz group). The algebra A consists of
distributions of densities with singularities in the closed future light cone
subset. On account of the local isomorphism M = Spec(A), the quantum fields
exist only in the space-time manifold with the one-dimensional arrow of time.
In the fermion sector the restrictions caused by the possibility to define the
multiplication on the densities of spinor fields can explain the chirality
violation. It is found that for bosons in the Higgs sector the charge
conjugation symmetry violation on the densities of states can be observed. This
symmetry violation can explain the matter-antimatter imbalance.

General Physics