Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants

Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants

It is shown that the group of generalized Lorentz transformations serves as the relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous breaking of initial gauge symmetry and from the formation...

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Date:2005
Main Author: Bogoslovsky, G.
Format: Article
Language:English
Published: Інститут математики НАН України 2005
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/209343
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants / G. Bogoslovsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 15 назв. — англ.

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spelling nasplib_isofts_kiev_ua-123456789-2093432025-11-20T01:01:07Z Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants Bogoslovsky, G. It is shown that the group of generalized Lorentz transformations serves as the relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous breaking of initial gauge symmetry and from the formation of an anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables the exact taking into account of the influence of the condensate on the dynamics of fundamental fields. In particular, the corresponding generalized Dirac equation turns out to be nonlinear. We have found two noncompact subgroups of the group of generalized Lorentz symmetry and their geometric invariants. These subgroups play a key role in constructing exact solutions of such equations. The author is grateful to Prof. H. Goenner for the fruitful collaboration that led to the results presented in this paper. It is a pleasure to thank Prof. R. Tavakol for helpful discussions. 2005 Article Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants / G. Bogoslovsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 15 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 53C60; 53C80 https://nasplib.isofts.kiev.ua/handle/123456789/209343 https://doi.org/10.3842/SIGMA.2005.017 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description It is shown that the group of generalized Lorentz transformations serves as the relativistic symmetry group of a flat Finslerian event space. Being the generalization of Minkowski space, the Finslerian event space arises from the spontaneous breaking of initial gauge symmetry and from the formation of an anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables the exact taking into account of the influence of the condensate on the dynamics of fundamental fields. In particular, the corresponding generalized Dirac equation turns out to be nonlinear. We have found two noncompact subgroups of the group of generalized Lorentz symmetry and their geometric invariants. These subgroups play a key role in constructing exact solutions of such equations.
format Article
author Bogoslovsky, G.
spellingShingle Bogoslovsky, G.
Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Bogoslovsky, G.
author_sort Bogoslovsky, G.
title Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
title_short Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
title_full Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
title_fullStr Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
title_full_unstemmed Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
title_sort subgroups of the group of generalized lorentz transformations and their geometric invariants
publisher Інститут математики НАН України
publishDate 2005
url https://nasplib.isofts.kiev.ua/handle/123456789/209343
citation_txt Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants / G. Bogoslovsky // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 15 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT bogoslovskyg subgroupsofthegroupofgeneralizedlorentztransformationsandtheirgeometricinvariants
first_indexed 2025-11-24T11:40:39Z
last_indexed 2025-11-24T11:40:39Z
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