On dynamical realizations of l-conformal Galilei and Newton–Hooke algebras; Nuclear Physics B; Vol. 896

On dynamical realizations of l-conformal Galilei and Newton–Hooke algebras; Nuclear Physics B; Vol. 896

Bibliographic Details
Parent link:Nuclear Physics B: Scientific Journal.— , 1956-
Vol. 896.— 2015.— [P. 244–254]
Main Author: Galajinsky A. V. Anton Vladimirovich
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Физико-технический институт (ФТИ) Кафедра высшей математики и математической физики (ВММФ)
Other Authors: Masterov I. V. Ivan Viktorovich
Summary:Title screen
In 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 .
Language:English
Published: 2015
Subjects:
труды учёных ТПУ
электронный ресурс
алгебра Галилея
дифференциальные уравнения второго порядка
уравнение Шредингера
гамильтонианы
Online Access:http://earchive.tpu.ru/handle/11683/35968
http://dx.doi.org/10.1016/j.nuclphysb.2015.04.024
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=644111

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