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...

Recent years have seen a renewed interest in experimental tests of Lorentz and CPT symmetry. Observable signals of Lorentz and CPT violation can be described in a modelindependent way using effective field theory (Kostelecký and Potting, 1995). The general realistic effective field theory for Lorentz violation is called the standard-model extension (SME) (Colladay and Kostelecký, 1997; 1998; Ko...

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric standard model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultraviolet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative correcti...

This talk summarizes some theoretical features and experimental implications of a general Lorentz-violating extension of the minimal SU(3) × SU(2)× U(1) standard model that allows for both CPT-even and CPT-odd effects. The theory would arise as the low-energy limit of a fundamental theory that is Lorentz and CPT covariant but in which spontaneous Lorentz breaking occurs. The use of neutral-meso...

Stokes parameters form a Minkowskian 4-vector under various optical transformations. As a consequence, the resulting two-by-two density matrix constitutes a representation of the Lorentz group. The associated Poincaré sphere is a geometric representation of the Lorentz group. Since the Lorentz group preserves the determinant of the density matrix, it cannot accommodate the decoherence process t...