‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...

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 ...

This paper derives equations for generalized Lorentz coordinate transformation based on a simple principle that only the wave equation must be form invariant and valid in both coordinate systems. The usual requirement that the speed of light is a universal constant and thus has an identical value in any inertial coordinate systems is removed. This leads to some interesting conclusions and possi...

We define Lorentz-transformation windows as windows that change the direction of transmitted light rays like a Lorentz transformation. Similarly, Galileo-transformation windows change the direction of transmitted light rays like a Galileo transformation. This light-ray-direction change distorts the scene seen through such a window in the same way in which the scene would be distorted in a photo...

We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and observe that this corresponds to a breaking of the Lorentz gauge condition by SUSY. Reasoning by analogy with SUSY’s violation of the Wess-Zumino gauge, we argue that the SUSY transformation, already modified to preserve Wess-Zumino gauge, should be further modified by another gauge transformation which restores the L...

The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial observers; (ii) Uniqueness, that is the condition that the Lorentz Transformation should be a single valued function of its arguments; (iii) Spatial Isotropy. It is a...