dc.identifier.uri |
http://dx.doi.org/10.15488/17116 |
|
dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/17244 |
|
dc.contributor.author |
Correa, Francisco
|
|
dc.contributor.author |
Leal, Gonzalo
|
|
dc.contributor.author |
Lechtenfeld, Olaf
|
|
dc.contributor.author |
Marquette, Ian
|
|
dc.date.accessioned |
2024-04-18T05:40:08Z |
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dc.date.available |
2024-04-18T05:40:08Z |
|
dc.date.issued |
2024 |
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dc.identifier.citation |
Correa, F.; Leal, G.; Lechtenfeld, O.; Marquette, I.: A Casimir operator for a Calogero W algebra. In: Journal of Physics A: Mathematical and Theoretical 57 (2024), Nr. 8, 085203. DOI: https://doi.org/10.1088/1751-8121/ad24ca |
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dc.description.abstract |
We investigate the nonlinear algebra W 3 generated by the 9 functionally independent permutation-symmetric operators in the three-particle rational quantum Calogero model. Decoupling the center of mass, we pass to a smaller algebra W 3 ′ generated by 7 operators, which fall into a spin-1 and a spin- 3 2 representation of the conformal sl(2) subalgebra. The commutators of the spin- 3 2 generators with each other are quadratic in the spin-1 generators, with a central term depending on the Calogero coupling. One expects this algebra to feature three Casimir operators, and we construct the lowest one explicitly in terms of Weyl-ordered products of the 7 generators. It is a polynomial of degree 6 in these generators, with coefficients being up to quartic in ℏ and quadratic polynomials in the Calogero coupling ℏ 2 g ( g − 1 ) . Putting back the center of mass, our Casimir operator for W 3 is a degree-9 polynomial in the 9 generators. The computations require the evaluation of nested Weyl orderings. The classical and free-particle limits are also given. Our scheme can be extended to any finite number N of Calogero particles and the corresponding nonlinear algebras WN and W N ′ . |
eng |
dc.language.iso |
eng |
|
dc.publisher |
Bristol : IOP Publ. |
|
dc.relation.ispartofseries |
Journal of Physics A: Mathematical and Theoretical 57 (2024), Nr. 8 |
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dc.rights |
CC BY 4.0 Unported |
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dc.rights.uri |
https://creativecommons.org/licenses/by/4.0 |
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dc.subject |
Calogero model |
eng |
dc.subject |
Casimir operator |
eng |
dc.subject |
W algebra |
eng |
dc.subject.ddc |
530 | Physik
|
|
dc.title |
A Casimir operator for a Calogero W algebra |
eng |
dc.type |
Article |
|
dc.type |
Text |
|
dc.relation.essn |
1751-8121 |
|
dc.relation.issn |
1751-8113 |
|
dc.relation.doi |
https://doi.org/10.1088/1751-8121/ad24ca |
|
dc.bibliographicCitation.issue |
8 |
|
dc.bibliographicCitation.volume |
57 |
|
dc.bibliographicCitation.firstPage |
085203 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|