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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209343 |
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| Zitieren: | 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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Bogoslovsky, G. 2025-11-19T12:24:19Z 2005 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants |
| spellingShingle |
Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants Bogoslovsky, G. |
| 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 |
| author |
Bogoslovsky, G. |
| author_facet |
Bogoslovsky, G. |
| publishDate |
2005 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| 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. |
| work_keys_str_mv |
AT bogoslovskyg subgroupsofthegroupofgeneralizedlorentztransformationsandtheirgeometricinvariants |
| first_indexed |
2025-11-24T11:40:39Z |
| last_indexed |
2025-11-24T11:40:39Z |
| _version_ |
1850885959160168448 |