Related papers: Generalized Komar currents for vector fields

We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.

The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.

Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…

The virial theorem is formulated both intrinsically and in local coordinates for a Lagrangian system of mechanical type on a Riemann manifold. An import case studied in this paper is that of an affine virial function associated to a vector…

We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we…

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…

We construct a Floer type boundary operator for generalised Morse-Smale dynamical systems on compact smooth manifolds by counting the number of suitable flow lines between closed (both homoclinic and periodic) orbits and isolated critical…

A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…

The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any…

We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order…

Courses in introductory special and general relativity have increasingly become part of the curriculum for upper-level undergraduate physics majors and master's degree candidates. One of the topics rarely discussed is symmetry, particularly…

Motivated by the possible characterization of Sasakian manifolds in terms of twistor forms, we give the complete classification of compact Riemannian manifolds carrying a Killing vector field whose covariant derivative (viewed as a 2-form)…

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the…

We construct a variety of conserved currents for test electromagnetic fields on a Kerr background. Our procedure, which involves the symplectic product for electromagnetism and symmetry operators, generates the conserved currents given by…

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We…

In classical and quantum mechanical systems on manifolds with gauge-field fluxes, constants of motion are constructed from gauge-covariant extensions of Killing vectors and tensors. This construction can be carried out using a manifestly…

The comprehensive generalization of summation-by-parts of Del Rey Fern\'andez et al.\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of…

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are…

It has been known that warped-product spacetimes such as spherically symmetric ones admit the Kodama vector. This vector provides a locally conserved current made by contraction of the Einstein tensor, even though there is no Killing…

Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved…