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001			644111
005			20231030040608.0
035			_a(RuTPU)RU\TPU\network\9160
090			_a644111
100			_a20151028a2015 k |0engy50 ba
101	1		_aeng
102			_aNL
135			_adrcn ---uucaa
181		0	_ai
182		0	_ab
200	1		_aOn dynamical realizations of l-conformal Galilei and Newton–Hooke algebras _fA. V. Galajinsky, I. V. Masterov
203			_aText _celectronic
300			_aTitle screen
320			_a[References: p. 253-254 (17 tit.)]
330			_aIn two recent papers (Aizawa et al., 2013 [15]) and (Aizawa et al., 2015 [16]), representation theory ofthe centrally extended l-conformal Galilei algebra with half-integer l has been applied so as to constructsecond order differential equations exhibiting the corresponding group as kinematical symmetry. It wassuggested to treat them as the Schrodinger equations which involve Hamiltonians describing dynamicalsystems without higher derivatives. The Hamiltonians possess two unusual features, however. First, theyinvolve the standard kinetic term only for one degree of freedom, while the remaining variables providecontributions linear in momenta. This is typical for Ostrogradsky’s canonical approach to the description ofhigher derivative systems. Second, the Hamiltonian in the second paper is not Hermitian in the conventionalsense. In this work, we study the classical limit of the quantum Hamiltonians and demonstrate that the firstof them is equivalent to the Hamiltonian describing free higher derivative nonrelativistic particles, whilethe second can be linked to the Pais–Uhlenbeck oscillator whose frequencies form the arithmetic sequence?k = (2k ? 1), k = 1,..., n. We also confront the higher derivative models with a genuine second ordersystem constructed in our recent work (Galajinsky and Masterov, 2013 [5]) which is discussed in detailfor l = 32 .
461			_tNuclear Physics B _oScientific Journal _d1956-
463			_tVol. 896 _v[P. 244–254] _d2015
610	1		_aтруды учёных ТПУ
610	1		_aэлектронный ресурс
610	1		_aалгебра Галилея
610	1		_aдифференциальные уравнения второго порядка
610	1		_aуравнение Шредингера
610	1		_aгамильтонианы
700		1	_aGalajinsky _bA. V. _cDoctor 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) _cProfessor of the TPU _f1971- _gAnton Vladimirovich _2stltpush _3(RuTPU)RU\TPU\pers\27878
701		1	_aMasterov _bI. V. _cphysicist _cassistant at Tomsk Polytechnic University _f1987- _gIvan Viktorovich _2stltpush _3(RuTPU)RU\TPU\pers\35458
712	0	2	_aНациональный исследовательский Томский политехнический университет (ТПУ) _bФизико-технический институт (ФТИ) _bКафедра высшей математики и математической физики (ВММФ) _h139 _2stltpush _3(RuTPU)RU\TPU\col\18727
801		2	_aRU _b63413507 _c20170112 _gRCR
856	4	0	_uhttp://earchive.tpu.ru/handle/11683/35968
856	4	0	_uhttp://dx.doi.org/10.1016/j.nuclphysb.2015.04.024
942			_cCF