Remarks on l-conformal extension of the Newton–Hooke algebra

Galajinsky, Anton; Masterov, Ivan

doi:10.1016/j.physletb.2011.06.093

Cited by 61 publications

(65 citation statements)

References 30 publications

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“…which perfectly agrees with the functions f H which again agrees with the fact that the dynamics of the considered model is related to the different choice of the basis of the conformal algebra H = ω(H + K) (as in the case of the harmonic and PU oscillators, see [23,48] and the references therein)…”

Section: Symmetries Of the Nonlocal Pu Model On The Lagrangian Levelsupporting

confidence: 84%

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

Andrzejewski

Bolonek-Lasoń

2016

Phys. Rev. D

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We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the non-relativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model and on the quantum level it leads to the centrally extended Virasoro algebra. *

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Section: Symmetries Of the Nonlocal Pu Model On The Lagrangian Levelsupporting

confidence: 84%

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

Andrzejewski

Bolonek-Lasoń

2016

Phys. Rev. D

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“…i are associated with space translations and Galilei boosts, while higher values of the index n correspond to accelerations (for more details see, e.g., [17]). 8 As usual, it suffices to verify that the corresponding gradients yield linearly independent vectors.…”

Section: Drach Systems and Higher Rank Killing Tensorsmentioning

confidence: 99%

Ricci-flat spacetimes admitting higher rank Killing tensors

Cariglia

Galajinsky

2015

Physics Letters B

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“…and computing the commutator [δ 1 , δ 2 ], one can then reproduce the conventional structure relations of the l = 3 2 conformal Galilei algebra [3]. Integrals of motion of the dynamical system (26) corresponding to the infinitesimal symmetry transformations displayed above read…”

Section: A Genuine Second Order Systemmentioning

confidence: 99%

“…One can verify that constants of the motion C (2) i and C (3) i which correspond to accelerations are functionally dependent on those related to conformal transformations, spatial translations and Galilei boosts…”

Section: A Genuine Second Order Systemmentioning

confidence: 99%

On dynamical realizations of l-conformal Galilei and Newton–Hooke algebras

Galajinsky

Masterov

2015

Nuclear Physics B

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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

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Remarks on l-conformal extension of the Newton–Hooke algebra

Abstract: The l-conformal extension of the Newton-Hooke algebra proposed in [J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro-KacMoody type extension is given.

Cited by 61 publications

References 30 publications

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

Ricci-flat spacetimes admitting higher rank Killing tensors

On dynamical realizations of l-conformal Galilei and Newton–Hooke algebras

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