Representations of the Schrödinger algebra and Appell systems
Identifieur interne : 006B42 ( Main/Exploration ); précédent : 006B41; suivant : 006B43Representations of the Schrödinger algebra and Appell systems
Auteurs : P. Feinsilver [États-Unis] ; J. Kocik [États-Unis] ; R. Schott [France]Source :
- Fortschritte der Physik [ 0015-8208 ] ; 2004-04-01.
English descriptors
- Teeft :
- Adjoint, Algebra, Appell, Appell polynomials, Appell system, Appell systems, Boson, Boson realization, Canonical, Canonical appell system, Canonical appell systems, Coherent states, Dinger, Dinger algebra, Evolution equations, Feinsilver, Fock space, Fortschr, Gmbh, Group calculations, Group element, Hermite polynomials, Hilbert, Hilbert space, Inner product, Kgaa, Leibniz, Leibniz formula, Leibniz function, Marginal distribution, Matrix, Matrix representation, Orthogonal, Orthogonal basis, Phys, Physical realization, Probabilistic interpretation, Random variables, Schr, Second kind, Special realization, Standard algebra, Standard form, Symmetry algebra, Verlag, Verlag gmbh, Weinheim, Weinheim fortschr, Wick products.
Abstract
We investigate the structure of the Schrödinger algebra. Two constructions are given that yield the physical realization via general methods starting from the abstract Lie algebra. Representations are found on a Fock space with basis given by a canonical Appell system. Generalized coherent states are used in the construction of the Hilbert space of functions on which certain commuting elements act as self‐adjoint operators. This yields a probabilistic interpretation of these operators as random variables. An interesting feature is how the semidirect product structure of the Lie algebra is reflected in the probability density function. A Leibniz function and orthogonal basis for the Hilbert space are found. Then certain evolution equations connected with canonical Appell systems on this algebra are shown.
Url:
DOI: 10.1002/prop.200310124
Affiliations:
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Two constructions are given that yield the physical realization via general methods starting from the abstract Lie algebra. Representations are found on a Fock space with basis given by a canonical Appell system. Generalized coherent states are used in the construction of the Hilbert space of functions on which certain commuting elements act as self‐adjoint operators. This yields a probabilistic interpretation of these operators as random variables. An interesting feature is how the semidirect product structure of the Lie algebra is reflected in the probability density function. A Leibniz function and orthogonal basis for the Hilbert space are found. Then certain evolution equations connected with canonical Appell systems on this algebra are shown.</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Grand Est</li><li>Illinois</li><li>Lorraine (région)</li></region><settlement><li>Vandoeuvre‐lès‐Nancy</li></settlement></list><tree><country name="États-Unis"><noRegion><name sortKey="Feinsilver, P" sort="Feinsilver, P" uniqKey="Feinsilver P" first="P." last="Feinsilver">P. Feinsilver</name></noRegion><name sortKey="Feinsilver, P" sort="Feinsilver, P" uniqKey="Feinsilver P" first="P." last="Feinsilver">P. Feinsilver</name><name sortKey="Feinsilver, P" sort="Feinsilver, P" uniqKey="Feinsilver P" first="P." last="Feinsilver">P. Feinsilver</name><name sortKey="Kocik, J" sort="Kocik, J" uniqKey="Kocik J" first="J." last="Kocik">J. Kocik</name></country><country name="France"><region name="Grand Est"><name sortKey="Schott, R" sort="Schott, R" uniqKey="Schott R" first="R." last="Schott">R. Schott</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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