title: Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors
metadata.name: dc.contributor.author
metadata.value: Monakhov, Vadim
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-11-14T10:55:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-11-14T10:55:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-07-20
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Monakhov, V. Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors. Universe 2019, 5, 162.
metadata.lang: en_GB
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16581
metadata.lang: -
metadata.name: dc.description
metadata.value: This is an open access article distributed under the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/ which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
metadata.lang: en_GB
metadata.name: dc.description.abstract
metadata.value: A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which we call gamma operators. Various field theory constructions are defined with use of these structures. We derive formulas for the vacuum state vector. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic approach as well as two additional operator analogs of gamma matrices, which are absent in the theory of Dirac spinors. We prove that there is a relationship between gamma operators and the most important physical operators of the second quantization method: number of particles, energy–momentum and electric charge operators. In addition to them, a series of similar operators are constructed from the creation and annihilation operators, which are Lorentz-invariant analogs of Dirac matrices. However, their physical meaning is not yet clear. We prove that the condition for the existence of spinor vacuum imposes restrictions on possible variants of the signature of the four-dimensional spacetime. It can only be (1, −1 , −1 , −1 ), and there are two additional axes corresponding to the inner space of the spinor, with a signature ( −1 , −1 ). Developed mathematical formalism allows one to obtain the second quantization operators in a natural way. Gauge transformations arise due to existence of internal degrees of freedom of superalgebraic spinors. These degrees of freedom lead to existence of nontrivial affine connections. Proposed approach opens perspectives for constructing a theory in which the properties of spacetime have the same algebraic nature as the momentum, electromagnetic field and other quantum fields.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: MDPI AG
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: spacetime signature; space-time signature; Clifford algebra; gamma matrices; Clifford vacuum; spinor vacuum; Clifford bundle; spinor bundle
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 2019_Monakhov_universe-05-00162.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16581/1/2019_Monakhov_universe-05-00162.pdf
resources.format: Adobe PDF
resources.description: Article Monakhov, V. Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors. Universe 2019, 5, 162.
resources.size: 349,81 kB