39 research outputs found
N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
We consider an N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator with
distinct frequencies of oscillation. The technique previously developed in
[Acta Phys. Polon. B 36 (2005) 2115; Nucl. Phys. B 902 (2016) 95] is used to
construct a family of Hamiltonian structures for this system.Comment: v1: 17 pages; v2: 18 pages; typos corrected, clarifying remarks
included into Section 3 and Conclusion; Section 5, references, and
acknowledgements added; published versio
An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
Ostrogradsky'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 [Acta Phys. Polon. B 36 (2005) 2115] 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.Comment: Typos corrected. Published versio
N=4 l-conformal Galilei superalgebra
An N=4 supersymmetric extension of the l-conformal Galilei algebra is
constructed. This is achieved by combining generators of spatial symmetries
from the l-conformal Galilei algebra and those underlying the most general
superconformal group in one dimension D(2,1;a). The value of the group
parameter a is fixed from the requirement that the resulting superalgebra is
finite-dimensional. The analysis reveals a=-1/2 thus reducing D(2,1;a) to
OSp(4|2).Comment: V3:11 pages. Two misprints in the introduction corrected. The version
to appear in PL
Dynamical realizations of l-conformal Newton-Hooke group
The method of nonlinear realizations and the technique previously developed
in 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=3/2-conformal Newton-Hooke symmetry for a particular choice of its
frequencies.Comment: 12 page
On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013)
405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015)
031701], representation theory of the centrally extended l-conformal Galilei
algebra with half-integer l has been applied so as to construct second order
differential equations exhibiting the corresponding group as kinematical
symmetry. It was suggested to treat them as the Schrodinger equations which
involve Hamiltonians describing dynamical systems without higher derivatives.
The Hamiltonians possess two unusual features, however. First, they involve the
standard kinetic term only for one degree of freedom, while the remaining
variables provide contributions linear in momenta. This is typical for
Ostrogradsky's canonical approach to the description of higher derivative
systems. Second, the Hamiltonian in the second paper is not Hermitian in the
conventional sense. In this work, we study the classical limit of the quantum
Hamiltonians and demonstrate that the first of them is equivalent to the
Hamiltonian describing free higher derivative nonrelativistic particles, while
the second can be linked to the Pais-Uhlenbeck oscillator whose frequencies
form the arithmetic sequence omega_k=(2k-1), k=1,...,n. We also confront the
higher derivative models with a genuine second order system constructed in our
recent work [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212] which is
discussed in detail for l=3/2.Comment: V2:12 pages,clarifying remarks included into the Introduction and
Conclusion, the version to appear in NP
Eisenhart lift for higher derivative systems
The Eisenhart lift provides an elegant geometric description of a dynamical
system of second order in terms of null geodesics of the Brinkmann-type metric.
In this work, we attempt to generalize the Eisenhart method so as to encompass
higher derivative models. The analysis relies upon Ostrogradsky's Hamiltonian.
A consistent geometric description seems feasible only for a particular class
of potentials. The scheme is exemplified by the Pais-Uhlenbeck oscillator.Comment: V2: 12 pages, minor improvements, references added; the version to
appear in PL
Towards -conformal Galilei algebra via contraction of the conformal group
We 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 page