Geometrical Applications of Split Octonions
It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1)-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these p...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/196708 |
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| author | Merab Gogberashvili Otari Sakhelashvili |
| author_facet | Merab Gogberashvili Otari Sakhelashvili |
| author_sort | Merab Gogberashvili |
| collection | DOAJ |
| description | It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1)-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. This group generates specific rotations of (3 + 4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentz-type rotations towards the extra time-like coordinates. It is shown how the G2 algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zero-norm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters. |
| format | Article |
| id | doaj-art-558f4a8bbd2a43a29744a48318d27896 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-558f4a8bbd2a43a29744a48318d278962025-02-03T01:28:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/196708196708Geometrical Applications of Split OctonionsMerab Gogberashvili0Otari Sakhelashvili1Tbilisi Ivane Javakhishvili State University, 3 Chavchavadze Avenue, 0179 Tbilisi, GeorgiaTbilisi Ivane Javakhishvili State University, 3 Chavchavadze Avenue, 0179 Tbilisi, GeorgiaIt is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1)-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. This group generates specific rotations of (3 + 4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentz-type rotations towards the extra time-like coordinates. It is shown how the G2 algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zero-norm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters.http://dx.doi.org/10.1155/2015/196708 |
| spellingShingle | Merab Gogberashvili Otari Sakhelashvili Geometrical Applications of Split Octonions Advances in Mathematical Physics |
| title | Geometrical Applications of Split Octonions |
| title_full | Geometrical Applications of Split Octonions |
| title_fullStr | Geometrical Applications of Split Octonions |
| title_full_unstemmed | Geometrical Applications of Split Octonions |
| title_short | Geometrical Applications of Split Octonions |
| title_sort | geometrical applications of split octonions |
| url | http://dx.doi.org/10.1155/2015/196708 |
| work_keys_str_mv | AT merabgogberashvili geometricalapplicationsofsplitoctonions AT otarisakhelashvili geometricalapplicationsofsplitoctonions |