BourbakiV1, France, Analysis, bibRecord, 000803

Minimal realizations and spectrum generating algebras

Identifieur interne : 000803 ( France/Analysis ); précédent : 000802; suivant : 000804

Minimal realizations and spectrum generating algebras

Auteurs : A. Joseph [France, Israël]

Source :

Communications in Mathematical Physics [ 0010-3616 ] ; 1974-12-01.

RBID : ISTEX:FF7D3D726944324064C5A189DCEA640B8B70E420

English descriptors

KwdEn :
- Algebra, Canonical, Canonical action, Canonical decomposition, Casimir invariants, Central element, Commutation relations, Complementary subspace, Complete dynkin diagram, Corresponding result, Differential operators, Dimensional representation, Hautes etudes, Heisenberg algebra, Heisenberg subalgebra, Highest root eigenvector, Homomorphic image, Hydrogen atom, Irreducible representation, Lowest root, Maximal commutative subalgebra, Minimal realization, Minimal realizations, Momentum space, Nuovo cimento, Parameter family, Phys, Physical importance, Polynomial algebra, Positive integer, Proper subalgebra, Quadratic casimir, Quantum mechanics, Quotient field, Real form, Real forms, Resp, Semisimple, Simple roots, Subalgebra, Such realizations, Theoretical physics, Weyl, Weyl algebra, Weyl group.
Teeft :
- Algebra, Canonical, Canonical action, Canonical decomposition, Casimir invariants, Central element, Commutation relations, Complementary subspace, Complete dynkin diagram, Corresponding result, Differential operators, Dimensional representation, Hautes etudes, Heisenberg algebra, Heisenberg subalgebra, Highest root eigenvector, Homomorphic image, Hydrogen atom, Irreducible representation, Lowest root, Maximal commutative subalgebra, Minimal realization, Minimal realizations, Momentum space, Nuovo cimento, Parameter family, Phys, Physical importance, Polynomial algebra, Positive integer, Proper subalgebra, Quadratic casimir, Quantum mechanics, Quotient field, Real form, Real forms, Resp, Semisimple, Simple roots, Subalgebra, Such realizations, Theoretical physics, Weyl, Weyl algebra, Weyl group.

Abstract

Abstract: The solution to the following problem is presented. Determine the least number of degrees of freedom for which a quantum mechanical system admits a given semisimple Lie algebra and construct the corresponding class of realizations. Such realizations are termed minimal realizations. It is shown that they can be obtained by a generalization of the inducing construction. Their physical importance is emphasized by showing that they possess most of the essential properties required of spectrum generating algebras.

Url:

https://api.istex.fr/document/FF7D3D726944324064C5A189DCEA640B8B70E420/fulltext/pdf

DOI: 10.1007/BF01646204

Affiliations:

France, Israël

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ISTEX:FF7D3D726944324064C5A189DCEA640B8B70E420

Le document en format XML

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<term>Central element</term>
<term>Commutation relations</term>
<term>Complementary subspace</term>
<term>Complete dynkin diagram</term>
<term>Corresponding result</term>
<term>Differential operators</term>
<term>Dimensional representation</term>
<term>Hautes etudes</term>
<term>Heisenberg algebra</term>
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<term>Homomorphic image</term>
<term>Hydrogen atom</term>
<term>Irreducible representation</term>
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<term>Physical importance</term>
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<term>Such realizations</term>
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<term>Central element</term>
<term>Commutation relations</term>
<term>Complementary subspace</term>
<term>Complete dynkin diagram</term>
<term>Corresponding result</term>
<term>Differential operators</term>
<term>Dimensional representation</term>
<term>Hautes etudes</term>
<term>Heisenberg algebra</term>
<term>Heisenberg subalgebra</term>
<term>Highest root eigenvector</term>
<term>Homomorphic image</term>
<term>Hydrogen atom</term>
<term>Irreducible representation</term>
<term>Lowest root</term>
<term>Maximal commutative subalgebra</term>
<term>Minimal realization</term>
<term>Minimal realizations</term>
<term>Momentum space</term>
<term>Nuovo cimento</term>
<term>Parameter family</term>
<term>Phys</term>
<term>Physical importance</term>
<term>Polynomial algebra</term>
<term>Positive integer</term>
<term>Proper subalgebra</term>
<term>Quadratic casimir</term>
<term>Quantum mechanics</term>
<term>Quotient field</term>
<term>Real form</term>
<term>Real forms</term>
<term>Resp</term>
<term>Semisimple</term>
<term>Simple roots</term>
<term>Subalgebra</term>
<term>Such realizations</term>
<term>Theoretical physics</term>
<term>Weyl</term>
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<front><div type="abstract" xml:lang="en">Abstract: The solution to the following problem is presented. Determine the least number of degrees of freedom for which a quantum mechanical system admits a given semisimple Lie algebra and construct the corresponding class of realizations. Such realizations are termed minimal realizations. It is shown that they can be obtained by a generalization of the inducing construction. Their physical importance is emphasized by showing that they possess most of the essential properties required of spectrum generating algebras.</div>
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Minimal realizations and spectrum generating algebras

Minimal realizations and spectrum generating algebras

Source :

English descriptors

Abstract

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