Related papers: The language of Einstein spoken by optical instrum…
We study the path of light rays passing near a massive object, in the context of the scale invariant equation of the geodesics first obtained by Dirac (1973). Using the exterior Schwarzschild solution for the metric, we derive the complete…
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein Gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin…
Since quarks are regarded as the most fundamental particles which constitute hadrons that we observe in the real world, there are many theories about how many of them are needed and what quantum numbers they carry. Another important…
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of…
The issue of implementing the principle of general relativity in Einstein equations has been widely discussed, since Kretschmann's well-known criticism stated that general covariance of the Einstein equations is not suffice to express the…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
In these notes we give an introductory unified treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocitiy addition, and gyrogroups and gyrovector spaces. An effort has been made to…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens…
Based on the principle of relativity with two universal constants (c, l) and in the inertial motion group IM(1,3)\sim PGL(5,R), with Lorentz isotropy, in addition to Poincar\'e group of Einstein's SR the dual Poincar\'e group preserves the…
Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…
Einstein's Equivalence Principle is used with the electromagnetic spectrum to translate meters and seconds into radians and seconds. Based on a unique geometric relationship, a new transformation of velocities and a changed Lorentz…
Einstein's equations with two commuting Killing vectors and the associated Lax pair are considered. The equations for the connection $A(\varsigma, \eta, \gamma)=\Psi_{,\gamma}\Psi^{-1}$, where $\gamma$ the variable spectral parameter are…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one…
Objecting that Sommerfeld's quantum conditions refer to particular coordinates, Einstein proposes a canonically invariant rule. But even if the invariance is canonical, Einstein may have in mind a double \emph{configuration} space…
Two-photon coherent states are one of the main building pillars of non-linear and quantum optics. It is the basis for the generation of minimum-uncertainty quantum states and entangled photon pairs, applications not obtainable from standard…
The theory of relativity was built up on linear Lorentz transformation. However, in his fundamental work "Theory of Space, Time and Gravitation" V.A.Fock shows that the general form of the transformation between the coordinates in the two…