相关论文: General Solutions of Relativistic Wave Equations

Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of…

We show that, at first order in the angular velocity, the general relativistic description of Rossby-Haurwitz waves (the analogues of r-waves on a thin shell) can be obtained from the corresponding Newtonian one after a coordinate…

We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a…

This brief note wants to bring to attention that the formulation of physically reasonable initial-boundary value problems for wave equations in Lorentzian space-times is not unique, i.e., that there are inequivalent such formulations that…

We study the most general, relativistic, constituent $q{\overline q}$ meson wave function within a new covariant framework. We find that by including a tensor wave function component, a pure valence quark model is now capable of reproducing…

The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…

The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…

The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…

The inner structure of the {\gamma}{\epsilon}-formalisms of Infeld and van der Waerden admits the occurrence of spin-tensor electromagnetic fields which bear invariance under the action of the generalized Weyl gauge group. A concise…

We use the $\mathbb T^2$-equivariant degree to establish the existence of unbounded branches of rotating spiral wave solutions with any number of arms for the complex Ginzburg Landau equation GLe on the planar unit disc, leveraging the…

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…

In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…

We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory for the wave equation on singular space-times.

Our contribution concerns with the numerical solution of the 3D general relativistic hydrodynamical system of equations within the framework of the 3+1 formalism. We summarize the theoretical ingredients which are necessary in order to…

The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis…

We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular…

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for…

We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…