Related papers: Lorentz transformation and vector field flows
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…
The Thomas precession is calculated using three different transformations to the rotating frame. It is shown that for sufficiently large values of $v/c$, important differences in the predicted angle of precession appear, depending on the…
In this article, matrix and vector formalisms for Lorentz transformations in time ($t$) and two space dimensions ($x$ and $y$) are developed and discussed. Lorentz transformations conserve the squared interval $t^2 - x^2 - y^2$. Examples of…
Starting from the well-known light-clock thought experiment to derive time dilation and length contraction, it is shown that finding the Lorentz Transformation requires nothing more than the most trivial vector addition formula. The form…
In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic…
Using the standard formalism of Lorentz transformation of the special theory of relativity, we derive the exact expression of the Thomas precession rate for an electron in a classical circular orbit around the nucleus of a hydrogen-like…
We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the…
We show that starting with the addition law of parallel speeds derived as a consequence of the invariance of the speed of light, the Lorentz transformations for the space-time coordinates can be derived.
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…
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.
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…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…
To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the…
The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions whose Lorentz-invariant coefficient functions…
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to…
It is recently discovered that the usual transformations of the three-dimensional (3D) vectors of the electric and magnetic fields differ from the Lorentz transformations (LT) (boosts) of the corresponding 4D quantities that represent the…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…