Related papers: Two-dimensional space-time symmetry in hyperbolic …

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…

The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…

In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly…

For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of…

We consider two strongly hyperbolic Hamiltonian formulations of general relativity and their numerical integration with a free and a partially constrained symplectic integrator. In those formulations we use hyperbolic drivers for the shift…

Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is…

We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which…

The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics…

We show exact dimensionality of harmonic measures associated with random walks on groups acting on a hyperbolic space under finite first moment condition, and establish the dimension formula by the entropy over the drift. We also treat the…

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…

There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…

Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying…

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…

We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a…

By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…

First, we extend the special relativity into the superluminal case and put forward a superluminal theory of kinematics, in which we show that the temporal coordinate need exchanging with one of the spatial coordinates in a superluminal…

In this paper, the Boiti Leon Pempinelli system in (2+1)-dimensions is revisited for Lie symmetries and invariant solutions. An infinite-dimensional Lie algebra is obtained using the Lie invariance criterion and is further classified into…

The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…