The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with...
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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147212 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra / K. Hallowell, A. Waldron // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147212 |
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dspace |
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irk-123456789-1472122019-02-14T01:23:30Z The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra Hallowell, K. Waldron, A. Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering. 2007 Article The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra / K. Hallowell, A. Waldron // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. 1815-0659 Waldron http://dspace.nbuv.gov.ua/handle/123456789/147212 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric tensor bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary tensor and spinor bundles using supersymmetric quantum mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric tensor setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering. |
| format |
Article |
| author |
Hallowell, K. Waldron, A. |
| spellingShingle |
Hallowell, K. Waldron, A. The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hallowell, K. Waldron, A. |
| author_sort |
Hallowell, K. |
| title |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra |
| title_short |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra |
| title_full |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra |
| title_fullStr |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra |
| title_full_unstemmed |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra |
| title_sort |
symmetric tensor lichnerowicz algebra and a novel associative fourier-jacobi algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147212 |
| citation_txt |
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra / K. Hallowell, A. Waldron // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:26:59Z |
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