Related papers: Lorentz transformations in time and two space dime…
The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects…
We show that alternative relativity theories that are essentially based on varied distant clock synchronization procedures can be recovered by using the standard Lorentz-Einstein transformations for the space-time coordinates of the same…
Orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of a Cantero-Moral-Velazquez moment matrix, which is constructed in terms of a complex…
The isometry-link problem is to determine all isometry transformations among given pair of vectors with the condition that if these initial and final vectors coincide, the transformation-link must be identity on entire vector space. In the…
Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin 1/2. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz…
A relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called…
In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz…
The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for the…
In this tutorial, exponentiation and factorization (decomposition) formulas are derived and discussed for common matrix operators that arise in studies of classical dynamics, linear and nonlinear optics, and special relativity. To…
In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel…
Lorentz Transformation is reinterpreted. It is shown that by admitting the existence of a frame of reference with synchronized clocks, we conclude that any other frame of reference that moves related to the first has desynchronized clocks.…
It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the three-parameter…
It is shown that the Lorentz group plays prominent roles in at least two areas in condensed matter physics, namely in the Bogoliubov transformation and optical filters. It is pointed out that the underlying symmetry of the Bogoliubov…
Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important…
The Lorentz transformation is derived without assuming the existence of Maxwell's equations, or that the speed of light is a constant, or even that light exists. This leads us logically to sonsider the existence of a primal field called…
In this work, it is shown that the energy and momentum of electromagnetic fields created by a classical charge, whose velocity varies with time, do not form four-vector. A possible explanation for this result is that the calculation of…
We present a formulation of a matrix model which manifestly possesses the general coordinate invariance when we identify the large $N$ matrices with differential operators. In order to build a matrix model which has the local Lorentz…
We relax the assumption of time translation and Lorentz boost symmetry in theories involving massless spin 2 gravitons, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. We project out…
We consider three possible approaches to formulating coordinate transformations on position space associated with non-linear Lorentz transformations on momentum space. The first approach uses the definition of velocity and gives the…