Eigenfunction Expansions of Functions Describing Systems with Symmetries

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dc.creatorKachuryk, Ivan
dc.creatorKlimyk, Anatoliy
dc.date2007-03-28
dc.date.accessioned2026-07-07T09:34:29Z
dc.date.available2026-07-07T09:34:29Z
dc.descriptionPhysical 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0703080
dc.identifierhttp://arxiv.org/abs/math-ph/0703080
dc.identifierSIGMA 3 (2007), 055, 84 pages
dc.identifierdoi:10.3842/SIGMA.2007.055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159509
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectRepresentation Theory
dc.titleEigenfunction Expansions of Functions Describing Systems with Symmetries
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