In their recent paper [8], Kulharni and Raymond show that a closed 3-manifold which admits a complete Lorentz metric of constant curvature 1 (henceforth called a complete Lorentz structure) must be Seifert fibered over a hyperbolic base. Furthermore on every such Seifert fibered 3-manifold with nonzero Euler class they construct such a Lorentz metric. Moreover the Lorentz structure they constru...

Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real 4-dimensional space-time. Bounded subsets of the real Lorentz group are retractable with arbitrary precision to finite subsets of such rational subgroups. These finite...

A hypothetical violation of Lorentz invariance in the electrons’ equation of motion (expressed within the Lorentz-violating extension of the standard model) leads to a change of the geometry of crystals and thus shifts the resonance frequency of an electromagnetic cavity. This allows experimental tests of Lorentz invariance of the electron sector of the standard model. The material dependence o...

The effect of Kerr nonlinearity on a Lorentz beam is investigated by using the nonlinear Schrödinger (NLS) equation. Based on the variational method, the evolution of a Lorentz beam in a Kerr medium is demonstrated and the critical collapse powers of the Lorentz beam are derived. Numerical simulations of the propagation of a Lorentz beam in a Kerr medium show that the beam becomes quasicircular...

the aim of this article is to extend the study of the lorentz transformation of order (m,n) from m=1 and n>=1 to all m,n>=1, obtaining algebraic structures called a bi-gyrogroup and a bi-gyrovector space. a bi-gyrogroup is a gyrogroup each gyration of which is a pair of a left gyration and a right gyration. a bi-gyrovector space is constructed from a bi-gyrocommutative bi-gyrogroup that admits ...

Partially coherent Lorentz-Gauss beams can propagate by remaining spatially localized and non-divergent. The Gaussian beams and after a bit application of Lorentz function, the Lorentz-Gauss beams are a better tool for optical communication. Analytical formulae for spatial complex degree of coherence are derived. In this paper mathematical model of Lorentz-Gauss beams is derived in terms of ABC...

In flat space, γ5 and the epsilon tensor break the dimensionally continued Lorentz symmetry in such a way that the propagators have fully Lorentz invariant denominators. When the Standard Model is coupled with quantum gravity γ5 breaks the continued local Lorentz symmetry. I show how to deform the Einstein lagrangian and gauge-fix the residual local Lorentz symmetry so that the propagators of t...

Abstract. In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing r...