Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00356913" target="_blank" >RIV/68407700:21240/22:00356913 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/22:00356913
Result on the web
<a href="https://doi.org/10.1088/1751-8121/ac515e" target="_blank" >https://doi.org/10.1088/1751-8121/ac515e</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ac515e" target="_blank" >10.1088/1751-8121/ac515e</a>

Result language
angličtina
Original language name
Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion
Original language description
Motivated by the consideration of integrable systems in three spatial dimensions in Euclidean space with integrals quadratic in the momenta we classify three-dimensional Abelian subalgebras of quadratic elements in the universal enveloping algebra of the Euclidean algebra under the assumption that the Casimir invariant (p) over right arrow . (l) over right arrow vanishes in the relevant representation. We show by means of an explicit example that in the presence of magnetic field, i.e. terms linear in the momenta in the Hamiltonian, this classification allows for pairs of commuting integrals whose leading order terms cannot be written in the famous classical form of Makarov et al [17]. We consider limits simplifying the structure of the magnetic field in this example and corresponding reductions of integrals, demonstrating that singularities in the integrals may arise, forcing structural changes of the leading order terms.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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