Mihai Visinescu

Spinning particles in Taub-NUT space

The geodesic motion of pseudoclassical spinning particles in Euclidean Taub-NUT space is analyzed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected.

Generalized Taub-NUT metrics and Killing-Yano tensors

The necessary condition that a Stackel-Killing tensor of valence two should be the contracted product of a Killing-Yano tensor of valence two with itself is rederived for a Riemannian manifold. This condition is applied to the generalized Euclidean Taub-NUT metrics which admit a Kepler-type symmetry. It is shown that, in general, the Stackel-Killing tensors involved in the Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The only exception is the original Taub-NUT metric.

Nonholonomic Ricci Flows and Running Cosmological Constant: I. 4D Taub-NUT Metrics

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four-dimensional (4D) Taub-NUT space–times. It is outlined a new geometric technique of constructing Ricci flow solutions. Some conceptual issues on space–times provided with generic off-diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/Ricci flow models with nontrivial torsion to configurations with the Levi-Civita connection is allowed in some specific physical circumstances by constraining the class of integral varieties for the Einstein and Ricci flow equations.

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 KillingYano tensors. The general results are applied to the case of the fourdimensional Euclidean Taub-NUT spinning space. A simple exact solution, corresponding to trajectories lying on a cone, is given..

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.

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.

HIGHER ORDER FIRST INTEGRALS OF MOTION IN A GAUGE COVARIANT HAMILTONIAN FRAMEWORK

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing–Yano tensors is pointed out. Some nontrivial examples involving Runge–Lenz type conserved quantities are explicitly worked out.

Dynamical algebra and Dirac quantum modes in the 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 the Taub-NUT background. The consequence is that there exist central and axial discrete modes whose spinors have no separated variables.

Runge–Lenz operator for Dirac field in Taub-NUT background

Abstract Fermions in D =4 self-dual Euclidean Taub-NUT space are investigated. Dirac-type operators involving Killing–Yano tensors of the Taub-NUT geometry are explicitly given showing that they anticommute with the standard Dirac operator and commute with the Hamiltonian as it is expected. They are connected with the hidden symmetries of the space allowing the construction of a conserved vector operator analogous to the Runge–Lenz vector of the Kepler problem. This operator is written down pointing out its algebraic properties.

Geodesic motion in Taub--NUT spinning space

The geodesic motion of pseudo-classical spinning particles in the Euclidean Taub--NUT space is analysed. The generalized Killing equations for spinning space are investigated and the constants of motion are derived in terms of the solutions of these equations. A simple exact solution, corresponding to trajectories lying on a cone, is given.