Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants
It is shown that the group of generalized Lorentz transformations serves as 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 a...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2005-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://www.emis.de/journals/SIGMA/2005/Paper017/ |
| _version_ | 1811277518875918336 |
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| author | George Bogoslovsky |
| author_facet | George Bogoslovsky |
| author_sort | George Bogoslovsky |
| collection | DOAJ |
| description | It is shown that the group of generalized Lorentz transformations serves as 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 anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables exact taking into account the influence of 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 equation. |
| first_indexed | 2024-04-13T00:18:08Z |
| format | Article |
| id | doaj.art-9da73839e9fb4880b750e6b5e3e2b2bc |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-13T00:18:08Z |
| publishDate | 2005-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-9da73839e9fb4880b750e6b5e3e2b2bc2022-12-22T03:10:52ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592005-11-011017Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric InvariantsGeorge BogoslovskyIt is shown that the group of generalized Lorentz transformations serves as 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 anisotropic fermion-antifermion condensate. The principle of generalized Lorentz invariance enables exact taking into account the influence of 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 equation.http://www.emis.de/journals/SIGMA/2005/Paper017/LorentzPoincaré and gauge invariancespontaneous symmetry breakingFinslerian space-time |
| spellingShingle | George Bogoslovsky Subgroups of the Group of Generalized Lorentz Transformations and Their Geometric Invariants Symmetry, Integrability and Geometry: Methods and Applications Lorentz Poincaré and gauge invariance spontaneous symmetry breaking Finslerian space-time |
| title | 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_short | 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 |
| topic | Lorentz Poincaré and gauge invariance spontaneous symmetry breaking Finslerian space-time |
| url | http://www.emis.de/journals/SIGMA/2005/Paper017/ |
| work_keys_str_mv | AT georgebogoslovsky subgroupsofthegroupofgeneralizedlorentztransformationsandtheirgeometricinvariants |