391 research outputs found
Killing forms on the five-dimensional Einstein-Sasaki Y(p,q) spaces
We present the complete set of Killing-Yano tensors on the five-dimensional
Einstein-Sasaki Y(p,q) spaces. Two new Killing-Yano tensors are identified,
associated with the complex volume form of the Calabi-Yau metric cone. The
corresponding hidden symmetries are not anomalous and the geodesic equations
are superintegrable.Comment: 10 pages; improved versio
Generalized Killing equations for spinning spaces and the role of Killing-Yano tensors
The generalized Killing equations for the configuration space of spinning
particles (spinning space) are analysed. Solutions of these equations are
expressed in terms of Killing-Yano tensors. In general the constants of motion
can be seen as extensions of those from the scalar case or new ones depending
on the Grassmann-valued spin variables.Comment: LaTeX, 6 pages, Talk given at the International Symposium on the
Theory of Elementary Particles, Buckow 199
On the Lattice Corrections to the Free Energy of Kink-Bearing Nonlinear One-Dimensional Scalar Systems
A ri proof of the effective potential (lattice corrections included) deduced
by Trullinger and Sasaki is given. Using asymptotic methods from the theory of
differential equations depending on a large parameter, the lattice corrections
to the kink and kink-kink contributions to the free energy are calculated. The
results are in complete agreement with a first order correction to the energy
of the static kink.Comment: 12 pages,plainte
Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
The Eisenhart-Duval lift allows embedding non-relativistic theories into a
Lorentzian geometrical setting. In this paper we study the lift from the point
of view of the Dirac equation and its hidden symmetries. We show that
dimensional reduction of the Dirac equation for the Eisenhart-Duval metric in
general gives rise to the non-relativistic Levy-Leblond equation in lower
dimension. We study in detail in which specific cases the lower dimensional
limit is given by the Dirac equation, with scalar and vector flux, and the
relation between lift, reduction and the hidden symmetries of the Dirac
equation. While there is a precise correspondence in the case of the lower
dimensional massive Dirac equation with no flux, we find that for generic
fluxes it is not possible to lift or reduce all solutions and hidden
symmetries. As a by-product of this analysis we construct new Lorentzian
metrics with special tensors by lifting Killing-Yano and Closed Conformal
Killing-Yano tensors and describe the general Conformal Killing-Yano tensor of
the Eisenhart-Duval lift metrics in terms of lower dimensional forms. Lastly,
we show how dimensionally reducing the higher dimensional operators of the
massless Dirac equation that are associated to shared hidden symmetries it is
possible to recover hidden symmetry operators for the Dirac equation with flux.Comment: 18 pages, no figures. Version 3: some typos corrected, some
discussions clarified, part of the abstract change
Supersymmetries and constants of motion in Taub-NUT spinning space
We review the geodesic motion of pseudo-classical spinning particles in
curved spaces. Investigating the generalized Killing equations for spinning
spaces, we express the constants of motion in terms of Killing-Yano tensors.
The general results are applied to the case of the four-dimensional Euclidean
Taub-NUT spinning space. A simple exact solution, corresponding to trajectories
lying on a cone, is given.Comment: 33 pages, LaTeX2e, to appear in Fortschritte der Physi
Statistical approach of the modulational instability of the discrete self-trapping equation
The discrete self-trapping equation (DST) represents an useful model for
several properties of one-dimensional nonlinear molecular crystals. The
modulational instability of DST equation is discussed from a statistical point
of view, considering the oscillator amplitude as a random variable. A kinetic
equation for the two-point correlation function is written down, and its linear
stability is studied. Both a Gaussian and a Lorentzian form for the initial
unperturbed wave spectrum are discussed. Comparison with the continuum limit
(NLS equation) is done.Comment: 10 page
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