Version 1
: Received: 9 July 2023 / Approved: 11 July 2023 / Online: 12 July 2023 (03:11:30 CEST)
How to cite:
Batanov-Gaukhman, M. Geometrized Vacuum Physics. Part II. Algebra of Signatures. Preprints2023, 2023070716. https://doi.org/10.20944/preprints202307.0716.v1
Batanov-Gaukhman, M. Geometrized Vacuum Physics. Part II. Algebra of Signatures. Preprints 2023, 2023070716. https://doi.org/10.20944/preprints202307.0716.v1
Batanov-Gaukhman, M. Geometrized Vacuum Physics. Part II. Algebra of Signatures. Preprints2023, 2023070716. https://doi.org/10.20944/preprints202307.0716.v1
APA Style
Batanov-Gaukhman, M. (2023). <strong></strong>Geometrized Vacuum Physics. Part II. Algebra of Signatures. Preprints. https://doi.org/10.20944/preprints202307.0716.v1
Chicago/Turabian Style
Batanov-Gaukhman, M. 2023 "<strong></strong>Geometrized Vacuum Physics. Part II. Algebra of Signatures" Preprints. https://doi.org/10.20944/preprints202307.0716.v1
Abstract
This article is the second part of a scientific project under the general name "Geometrized vacuum physics". On the basis of the Algebra of Stignatures presented in the previous article [1], this article develops the main provisions of the Algebra of Signatures. Both of the above algebras are aimed at studying the properties of an ideal vacuum, but at the same time they are universal and can be applied in various branches of knowledge. It is shown that the signature of a quadratic form is related to the topology of the metric space for which the given quadratic form is a metric. Conditions are given under which an additive imposition of metric spaces with different topologies (or signatures) leads to a total Ricci flat space similar to a Calabi-Yau manifold. A spin-tensor representation of metrics with different signatures is considered and a Dirac bundle of quadratic forms is presented. This article does not contain physical applications of the Algebra of Signatures, but the potential power of this mathematical apparatus will be demonstrated in subsequent articles of this project.
Keywords
vacuum; geometrized vacuum physics; signature; algebra of signature
Subject
Physical Sciences, Theoretical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
