Related papers: Duality properties of Gorringe-Leach equations
The field theoretical description of the general relativity (GR) is further developed. The action for the gravitational field and its sources is given explicitely. The equations of motion and the energy-momentum tensor for the gravitational…
P. Clarke describes mirror symmetry as a duality between Landau--Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective…
The dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making them functions of position. These…
Two spherically symmetric, static Lorentzian wormholes are obtained in tetrad theory of gravitation as a solution of the equation $\rho=\rho_t=0$, where $\rho=T_{ij}u^iu^j, \rho_t=(T_{ij}-{1/2}Tg_{ij})u^iu^j$ and $u^iu_i=-1$. This equation…
Starting from the Ashtekar Hamiltonian variables for general relativity, the self-dual Einstein equations (SDE) may be rewritten as evolution equations for three divergence free vector fields given on a three dimensional surface with a…
Applying the Sachs formalism, the optical properties encoded in the distance modulus are studied along curves exhibiting local rotational symmetry for some closed inhomogeneous cosmological models whose mass content is discretized by…
A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…
Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even…
Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and…
The invariance of the Lagrangian under time translations and rotations in Kepler's problem yields the conservation laws related to the energy and angular momentum. Noether's theorem reveals that these same symmetries furnish generalized…
We extend the Kerr-Schild double copy to the case of a probe particle moving in the Kerr-Schild background. In particular, we solve Wong's equations for a test color charge in a Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…
We present a solution to the problem of reflection/refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total…
The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This…
Given two equidimensional Cohen-Macaulay local rings of the same dimension, one shows that a simultaneous extension of each of them by a dualizing module of the other is Gorenstein. This generalizes a theorem of Fossum. The geometrical…
Lorentz's reciprocity lemma and Feld-Tai reciprocity theorem show the effect of interchanging the action and reaction in Maxwell's equations. We derive a free-space version of these reciprocity relations which generalizes the conservation…
We consider the Dirac equations in polar form proving that they can equivalently be re-configured into a system of equations consisting of derivatives of the velocity density plus the Hamilton-Jacobi equation, giving the momentum in terms…
No positive result has been obtained on the magnetic monopoles search. This allows to consider different theoretical approaches as the proposed in this paper, developed in the framework of the Einstein General Relativity. The properties of…
A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved,…