Eigenfunction Expansions of Functions Describing Systems with Symmetries
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of kinematical parts in the functions is fulfilled by means of harmoni...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-03-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/055/ |
| _version_ | 1811302938000228352 |
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| author | Ivan Kachuryk Anatoliy Klimyk |
| author_facet | Ivan Kachuryk Anatoliy Klimyk |
| author_sort | Ivan Kachuryk |
| collection | DOAJ |
| description | Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of kinematical parts in the functions is fulfilled by means of harmonic analysis related to the group $G$. This separation depends on choice of a coordinate system on the space where a physical system exists. In the paper we review how coordinate systems can be chosen and how the corresponding harmonic analysis can be done. In the first part we consider in detail the case when $G$ is the de Sitter group $SO_0(1,4)$. In the second part we show how the corresponding theory can be developed for any noncompact semisimple real Lie group. |
| first_indexed | 2024-04-13T07:39:25Z |
| format | Article |
| id | doaj.art-a77c88c1a3964ad19ace0469ff057345 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-04-13T07:39:25Z |
| publishDate | 2007-03-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-a77c88c1a3964ad19ace0469ff0573452022-12-22T02:55:59ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-03-013055Eigenfunction Expansions of Functions Describing Systems with SymmetriesIvan KachurykAnatoliy KlimykPhysical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of kinematical parts in the functions is fulfilled by means of harmonic analysis related to the group $G$. This separation depends on choice of a coordinate system on the space where a physical system exists. In the paper we review how coordinate systems can be chosen and how the corresponding harmonic analysis can be done. In the first part we consider in detail the case when $G$ is the de Sitter group $SO_0(1,4)$. In the second part we show how the corresponding theory can be developed for any noncompact semisimple real Lie group.http://www.emis.de/journals/SIGMA/2007/055/representationseigenfunction expansionspecial functionsde Sitter groupsemisimple Lie groupcoordinate systemsinvariant operators |
| spellingShingle | Ivan Kachuryk Anatoliy Klimyk Eigenfunction Expansions of Functions Describing Systems with Symmetries Symmetry, Integrability and Geometry: Methods and Applications representations eigenfunction expansion special functions de Sitter group semisimple Lie group coordinate systems invariant operators |
| title | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_full | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_fullStr | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_full_unstemmed | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_short | Eigenfunction Expansions of Functions Describing Systems with Symmetries |
| title_sort | eigenfunction expansions of functions describing systems with symmetries |
| topic | representations eigenfunction expansion special functions de Sitter group semisimple Lie group coordinate systems invariant operators |
| url | http://www.emis.de/journals/SIGMA/2007/055/ |
| work_keys_str_mv | AT ivankachuryk eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries AT anatoliyklimyk eigenfunctionexpansionsoffunctionsdescribingsystemswithsymmetries |