105 research outputs found
A variant of Schwarzian mechanics
The Schwarzian derivative is invariant under SL(2,R)-transformations and, as
thus, any function of it can be used to determine the equation of motion or the
Lagrangian density of a higher derivative SL(2,R)-invariant 1d mechanics or the
Schwarzian mechanics for short. In this note, we consider the simplest variant
which results from setting the Schwarzian derivative to be equal to a
dimensionful coupling constant. It is shown that the corresponding dynamical
system in general undergoes stable evolution but for one fixed point solution
which is only locally stable. Conserved charges associated with the
SL(2,R)-symmetry transformations are constructed and a Hamiltonian formulation
reproducing them is proposed. An embedding of the Schwarzian mechanics into a
larger dynamical system associated with the geodesics of a Brinkmann-like
metric obeying the Einstein equations is constructed.Comment: V2: 8 pages, typos fixed. The version to appear in NP
Remark on integrable deformations of the Euler top
The Euler top describes a free rotation of a rigid body about its center of
mass and provides an important example of a completely integrable system. A
salient feature of its first integrals is that, up to a reparametrization of
time, they uniquely determine the dynamical equations themselves. In this note,
this property is used to construct integrable deformations of the Euler top.Comment: V2:the version published in JMA
Geometry of the isotropic oscillator driven by the conformal mode
Geometrization of a Lagrangian conservative system typically amounts to
reformulating its equations of motion as the geodesic equations in a properly
chosen curved spacetime. The conventional methods include the Jacobi metric and
the Eisenhart lift. In this work, a modification of the Eisenhart lift is
proposed which describes the isotropic oscillator in arbitrary dimension driven
by the one-dimensional conformal mode.Comment: V3: 10 pages, presentation improved, the version to appear in Eur.
Phys. J.
N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets
N=4 supersymmetric extensions of the l-conformal Galilei algebra are
constructed by properly extending the Lie superalgebra associated with the most
general N=4 superconformal group in one dimension D(2,1;a). If the acceleration
generators in the superalgebra form analogues of the irreducible (1,4,3)-,
(2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a
turns out to be constrained by the Jacobi identities. In contrast, if the tower
of the acceleration generators resembles a component decomposition of a generic
real superfield, which is a reducible representation of D(2,1;a), a remains
arbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys.
Lett. B 771 (2017) 401] is shown to be a particular instance of a more general
construction in this work.Comment: V2: 9 pages. Introductory part extended, two references added. The
version to appear in JHE
Ricci-flat spacetimes admitting higher rank Killing tensors
Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which
admit irreducible Killing tensors of rank-3 or rank-4. The construction relies
upon the Eisenhart lift applied to Drach's two-dimensional integrable systems
which is followed by the oxidation with respect to free parameters. In four
dimensions, some of our solutions are anti-self-dual.Comment: 12 page
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
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