40 research outputs found
N=2 supersymmetric odd-order Pais–Uhlenbeck oscillator
No full textWe consider an N=2 supersymmetric odd-order Pais–Uhlenbeck oscillator with distinct frequencies of oscillation. The technique previously developed in [Bolonek and Kosinski (2005) [7]], [Masterov (2016) [10]] is used to construct a family of Hamiltonian structures for this system
Dynamical realizations of l-conformal Newton–Hooke group
No full textAbstractThe method of nonlinear realizations and the technique previously developed in [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212, arXiv:1208.1403] are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton–Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effective external field. The dynamical system describes a generalized multi-dimensional oscillator, which undergoes accelerated/decelerated motion in an ellipse in accord with evolution of the conformal mode. Higher derivative formulations are discussed as well. It is demonstrated that the multi-dimensional Pais–Uhlenbeck oscillator enjoys the l=32-conformal Newton–Hooke symmetry for a particular choice of its frequencies
An alternative Hamiltonian formulation for the Pais–Uhlenbeck oscillator
No full textAbstractOstrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais–Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [7] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais–Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N=2 supersymmetric Pais–Uhlenbeck oscillator
On dynamical realizations of l-conformal Galilei and Newton–Hooke algebras
No full textIn 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
The odd-order Pais–Uhlenbeck oscillator
No full textAbstractWe consider a Hamiltonian formulation of the (2n+1)-order generalization of the Pais–Uhlenbeck oscillator with distinct frequencies of oscillation. This system is invariant under time translations. However, the corresponding Noether integral of motion is unbounded from below and can be presented as a direct sum of 2n one-dimensional harmonic oscillators with an alternating sign. If this integral of motion plays a role of a Hamiltonian, a quantum theory of the Pais–Uhlenbeck oscillator faces a ghost problem. We construct an alternative canonical formulation for the system under study to avoid this nasty feature
Towards -conformal Galilei algebra via contraction of the conformal group
No full textWe show that the In\"{o}n\"{u}-Wigner contraction of with
the integer may lead to algebra which contains a variety of conformal
extensions of the Galilei algebra as subalgebras. These extensions involve the
-conformal Galilei algebra in spatial dimensions as well as
-conformal Galilei algebras in one spatial dimension with , , ...,
.Comment: 14 pages, typos correcte
