2017/09/28 by L. V. Lutsev, Lutsev, Leonid
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1709.10358
openalex publication_date 2017/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider properties of the space-time manifold M caused by\nthe proposition that, according to the scheme theory, the manifold M is locally\nisomorphic to the spectrum of the algebra A, M = Spec(A), where A is the\ncommutative algebra of distributions of quantum-field densities. In order to\ndetermine the algebra A, it is necessary to define multiplication on densities\nand to eliminate those densities, which cannot be multiplied. This leads to\nessential restrictions imposed on densities and on space-time properties. It is\nfound that the only possible case, when the commutative algebra A exists, is\nthe case, when the quantum fields are in the spacetime manifold M with the\nstructure group SO(3,1) (Lorentz group). The algebra A consists of\ndistributions of densities with singularities in the closed future light cone\nsubset. On account of the local isomorphism M = Spec(A), the quantum fields\nexist only in the space-time manifold with the one-dimensional arrow of time.\nIn the fermion sector the restrictions caused by the possibility to define the\nmultiplication on the densities of spinor fields can explain the chirality\nviolation. It is found that for bosons in the Higgs sector the charge\nconjugation symmetry violation on the densities of states can be observed. This\nsymmetry violation can explain the matter-antimatter imbalance.\n