Eisenhart lift of 2-dimensional mechanics; The European Physical Journal C; Vol. 79, iss. 4
| Parent link: | The European Physical Journal C: Scientific Journal Vol. 79, iss. 4.— 2019.— [301, 11 р.,] |
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| Riassunto: | Title screen The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on (d+2) -dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of 2-dimensional mechanics on curved background is studied. The corresponding 4-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy–momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of 2-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the 2-dimensional Darboux–Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented. Режим доступа: по договору с организацией-держателем ресурса |
| Lingua: | inglese |
| Pubblicazione: |
2019
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| Accesso online: | https://doi.org/10.1140/epjc/s10052-019-6812-6 |
| Natura: | Elettronico Capitolo di libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=660159 |
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| 200 | 1 | |a Eisenhart lift of 2-dimensional mechanics |f A. P. Fordy, A. V. Galajinsky | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 28 tit.] | ||
| 330 | |a The Eisenhart lift is a variant of geometrization of classical mechanics with d degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on (d+2) -dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of 2-dimensional mechanics on curved background is studied. The corresponding 4-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy–momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of 2-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the 2-dimensional Darboux–Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t The European Physical Journal C |o Scientific Journal | ||
| 463 | |t Vol. 79, iss. 4 |v [301, 11 р.,] |d 2019 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a лифт Эйзенхарта | |
| 610 | 1 | |a двухмерное проектирование | |
| 700 | 1 | |a Fordy |b A. P. | |
| 701 | 1 | |a Galajinsky |b A. V. |c Doctor of Physical and Mathematical Sciences, Tomsk Polytechnic University (TPU), Department of Higher Mathematics and Mathematical Physics of the Institute of Physics and Technology (HMMPD IPT) |c Professor of the TPU |f 1971- |g Anton Vladimirovich |3 (RuTPU)RU\TPU\pers\27878 |9 12894 | |
| 712 | 0 | 2 | |a Национальный исследовательский Томский политехнический университет |b Исследовательская школа физики высокоэнергетических процессов |c (2017- ) |3 (RuTPU)RU\TPU\col\23551 |
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| 856 | 4 | |u https://doi.org/10.1140/epjc/s10052-019-6812-6 | |
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