Three-dimensional superintegrable systems in a static electromagnetic field
We consider a charged particle moving in a static electromagnetic field described by the vector potential and the electrostatic potential We study the conditions on the structure of the integrals of motion of the first and second order in momenta, in particular how they are influenced by the gauge i...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-10, Vol.48 (39), p.395206-24 |
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| container_title | Journal of physics. A, Mathematical and theoretical |
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| creator | Marchesiello, A Šnobl, L Winternitz, P |
| description | We consider a charged particle moving in a static electromagnetic field described by the vector potential and the electrostatic potential We study the conditions on the structure of the integrals of motion of the first and second order in momenta, in particular how they are influenced by the gauge invariance of the problem. Next, we concentrate on the three possibilities for integrability arising from the first order integrals corresponding to three nonequivalent subalgebras of the Euclidean algebra, namely and For these cases we look for additional independent integrals of first or second order in the momenta. These would make the system superintegrable (minimally or maximally). We study their quantum spectra and classical equations of motion. In some cases nonpolynomial integrals of motion occur and ensure maximal superintegrability. |
| doi_str_mv | 10.1088/1751-8113/48/39/395206 |
| format | Article |
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Next, we concentrate on the three possibilities for integrability arising from the first order integrals corresponding to three nonequivalent subalgebras of the Euclidean algebra, namely and For these cases we look for additional independent integrals of first or second order in the momenta. These would make the system superintegrable (minimally or maximally). We study their quantum spectra and classical equations of motion. 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In some cases nonpolynomial integrals of motion occur and ensure maximal superintegrability.</description><subject>Algebra</subject><subject>classical and quantum mechanics</subject><subject>Electromagnetic fields</subject><subject>Equations of motion</subject><subject>Gauge invariance</subject><subject>integrability</subject><subject>Integrals</subject><subject>magnetic field</subject><subject>Mathematical analysis</subject><subject>Spectra</subject><subject>superintegrability</subject><subject>Three dimensional</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNqFkE1PwzAMhiMEEmPwF1CPXMripB_JEU18iUlcxjlKU3dk6hdxe9i_p1UnrkiWbMvv48PD2D3wR-BKbSBPIVYAcpOojdRTpYJnF2x1Pgi4_JtBXrMboiPnacK1WLGP_XdAjEvfYEu-a20d0dhj8O2Ah2CLGiM60YANRb6NbESDHbyLsEY3hK6xhxbnvfJYl7fsqrI14d25r9nXy_N--xbvPl_ft0-72MlcD7FzNiug5DpVBc8KJypMdJWjRisklIrbHItcWCFsKSvgaVaIwgGqzIHkwso1e1j-9qH7GZEG03hyWNe2xW4kAwpSrbJcyymaLVEXOqKAlemDb2w4GeBmtmdmMWYWYxJlpDaLvQkUC-i73hy7MUxm6D_oF5XDcsk</recordid><startdate>20151002</startdate><enddate>20151002</enddate><creator>Marchesiello, A</creator><creator>Šnobl, L</creator><creator>Winternitz, P</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20151002</creationdate><title>Three-dimensional superintegrable systems in a static electromagnetic field</title><author>Marchesiello, A ; Šnobl, L ; Winternitz, P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-cca6b1d0958b06bc2fe49f7e9ea231d80a7eb72a22ad3f1056b2bc1e86c1302a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algebra</topic><topic>classical and quantum mechanics</topic><topic>Electromagnetic fields</topic><topic>Equations of motion</topic><topic>Gauge invariance</topic><topic>integrability</topic><topic>Integrals</topic><topic>magnetic field</topic><topic>Mathematical analysis</topic><topic>Spectra</topic><topic>superintegrability</topic><topic>Three dimensional</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Marchesiello, A</creatorcontrib><creatorcontrib>Šnobl, L</creatorcontrib><creatorcontrib>Winternitz, P</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of physics. 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| subjects | Algebra classical and quantum mechanics Electromagnetic fields Equations of motion Gauge invariance integrability Integrals magnetic field Mathematical analysis Spectra superintegrability Three dimensional |
| title | Three-dimensional superintegrable systems in a static electromagnetic field |
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