Abstract
In this paper we consider properties of the four-dimensional 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. Points of the manifold M are defined as maximal ideals of density distributions. 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 space-time 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. It is found that in theoretical models with non-abelian gauge fields instanton distributions are impossible and tunneling effects between different topological vacua | n> do not occur. Diagram expansion with respect to the -algebra variables is considered.
Highlights
The origin of the arrow of time, the possibility of physics in multiple time dimensions, the violation of the parity principle, and the matter-antimatter imbalance are ones of the most exciting and difficult challenges of physics.Physics in multiple time dimensions leads to new insights and, at the same time, contains theoretical problems
It is found that the only possible case, when the commutative algebra exists, is the case, when the quantum fields are in the space-time manifold with the structure group SO (3,1)
It is found that the only possible case, when the commutative algebra of distributions of quantum-field densities exists, is the case, when the quantum fields are in the space-time manifold with the structure group
Summary
The origin of the arrow of time, the possibility of physics in multiple time dimensions, the violation of the parity principle, and the matter-antimatter imbalance are ones of the most exciting and difficult challenges of physics. A particle can move in the causal region faster than the speed of light in vacuum This leads to contradictoriness of the multidimensional time theory and, at present, these problems have not been solved. In this paper we consider the above-mentioned space-time properties (the arrow of time, multiple time dimensions, and the chirality violation), the violation of the charge conjugation, and find that in the framework of the scheme theory. The asymmetry of time, the chirality violation of spinor fields, and the charge conjugation symmetry violation in the boson sector are the necessary conditions for the existence of
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