Related papers: Lorentz transformation from an elementary point of…
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
In the present study, we analyze in combination the principles of special relativity and the phenomenon of the aberration of light, deriving a system of equations that allows establishing the relationship between the angles commonly…
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…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted sl_N-valued…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
We consider the magneto-electric optical properties of the quantum vacuum and show that all the different phenomenona are related by Lorentz invariance. As a model calculation we show how crossed fields properties can be calculated starting…
We report the simplest possible form to compute rotations around arbitrary axis and boosts in arbitrary directions for 4-vectors (space-time points, energy-momentum) and bi-vectors (electric and magnetic field vectors) by symplectic…
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a…
Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum.…
In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion…
Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
We point out, by exhibiting two examples and mentioning a third one, that it is sometimes useful to consider Lorentz transformations as generated from hyperplane or line reflections. One example concerns the construction of boosts linking…
It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over…
In this work, we provide a detailed analysis of the issue of encoding of quantum information which is invariant with respect to arbitrary Lorentz transformations. We significantly extend already known results and provide compliments where…
We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well separated components and…
In this work, we demonstrate explicitly the unified nature of electric and magnetic fields, from the principles of special relativity and Lorentz transformations of the electromagnetic field tensor. Using an operational approach we…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…