133 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
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
Irreducible Killing Tensors from Third Rank Killing-Yano Tensors
We investigate higher rank Killing-Yano tensors showing that third rank
Killing-Yano tensors are not always trivial objects being possible to construct
irreducible Killing tensors from them. We give as an example the Kimura IIC
metric were from two rank Killing-Yano tensors we obtain a reducible Killing
tensor and from third rank Killing-Yano tensors we obtain three Killing
tensors, one reducible and two irreducible.Comment: 10 page
Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
Hidden symmetries in a covariant Hamiltonian formulation are investigated
involving gauge covariant equations of motion. The special role of the
Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce
the original phase space to another one in which the symmetries are divided
out. The reverse of the reduction procedure is done by stages performing the
unfolding of the gauge transformation followed by the Eisenhart lift in
connection with scalar potentials.Comment: 15 pages; based on a talk at QTS-7 Conference, Prague, August 7-13,
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Spinning particles in Taub-NUT space
The geodesic motion of pseudo-classical spinning particles in Euclidean
Taub-NUT space is analysed. The constants of motion are expressed in terms of
Killing-Yano tensors. Some previous results from the literature are corrected.Comment: LaTeX, 8 page
Generalized Killing equations and Taub-NUT spinning space
The generalized Killing equations for the configuration space of spinning
particles (spinning space) are analysed. Simple solutions of the homogeneous
part of these equations are expressed in terms of Killing-Yano tensors. The
general results are applied to the case of the four-dimensional euclidean
Taub-NUT manifold.Comment: 10 pages, late
Dynamical algebra and Dirac quantum modes in Taub-NUT background
The SO(4,1) gauge-invariant theory of the Dirac fermions in the external
field of the Kaluza-Klein monopole is investigated. It is shown that the
discrete quantum modes are governed by reducible representations of the o(4)
dynamical algebra generated by the components of the angular momentum operator
and those of the Runge-Lenz operator of the Dirac theory in Taub-NUT
background. The consequence is that there exist central and axial discrete
modes whose spinors have no separated variables.Comment: 17 pages, latex, no figures. Version to appear in Class.Quantum Gra
Fermion on curved spaces, symmetries, and quantum anomalies
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. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. The gravitational and axial anomalies are studied for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. Using the Atiyah-Patodi-Singer index theorem for manifolds with boundaries, it is shown that the these metrics make no contribution to the axial anomaly
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