Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields
Maxwell’s vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators (integrals of motion) that is isomorphic to the algebra of group operators. Two fram...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/4/245 |
| _version_ | 1827619433915351040 |
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| author | Valery V. Obukhov |
| author_facet | Valery V. Obukhov |
| author_sort | Valery V. Obukhov |
| collection | DOAJ |
| description | Maxwell’s vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators (integrals of motion) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell’s equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity. |
| first_indexed | 2024-03-09T10:28:05Z |
| format | Article |
| id | doaj.art-5829fc372a0a4ce7a09ce223891f4dcc |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T10:28:05Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-5829fc372a0a4ce7a09ce223891f4dcc2023-12-01T21:30:05ZengMDPI AGUniverse2218-19972022-04-018424510.3390/universe8040245Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic FieldsValery V. Obukhov0Institute of Scientific Research and Development, Tomsk State Pedagogical University, Tomsk 634041, RussiaMaxwell’s vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators (integrals of motion) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell’s equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity.https://www.mdpi.com/2218-1997/8/4/245Maxwell’s vacuum equationsHamilton–Jacobi equationKlein–Gordon–Fock equationalgebra of symmetry operatorsseparation of variableslinear partial differential equations |
| spellingShingle | Valery V. Obukhov Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields Universe Maxwell’s vacuum equations Hamilton–Jacobi equation Klein–Gordon–Fock equation algebra of symmetry operators separation of variables linear partial differential equations |
| title | Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields |
| title_full | Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields |
| title_fullStr | Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields |
| title_full_unstemmed | Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields |
| title_short | Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields |
| title_sort | maxwell s equations in homogeneous spaces for admissible electromagnetic fields |
| topic | Maxwell’s vacuum equations Hamilton–Jacobi equation Klein–Gordon–Fock equation algebra of symmetry operators separation of variables linear partial differential equations |
| url | https://www.mdpi.com/2218-1997/8/4/245 |
| work_keys_str_mv | AT valeryvobukhov maxwellsequationsinhomogeneousspacesforadmissibleelectromagneticfields |