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In this paper we consider properties of the space-time manifold M caused bythe proposition that, according to the scheme theory, the manifold M is locallyisomorphic to the spectrum of the algebra A, M = Spec(A), where A is thecommutative algebra of distributions of quantum-field densities. In order todetermine the algebra A, it is necessary to define multiplication on densitiesand to eliminate those densities, which cannot be multiplied. This leads toessential restrictions imposed on densities and on space-time properties. It isfound that the only possible case, when the commutative algebra A exists, isthe case, when the quantum fields are in the spacetime manifold M with thestructure group SO(3,1) (Lorentz group). The algebra A consists ofdistributions of densities with singularities in the closed future light conesubset. On account of the local isomorphism M = Spec(A), the quantum fieldsexist 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 themultiplication on the densities of spinor fields can explain the chiralityviolation. It is found that for bosons in the Higgs sector the chargeconjugation symmetry violation on the densities of states can be observed. Thissymmetry violation can explain the matter-antimatter imbalance.

Algebra of distributions of quantum-field densities and space-time properties