Related papers: Coordinate transformations in quaternion spaces
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
A relativistic transformation of the electrode potential has been derived to account for time dilation effects in electrode processes. This newly formulated Lorentz transformation is interpreted in terms of the generation of spin-2 boson…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
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…
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean…
A model of graviton momentum transfer was constructed to investigate a conjecture that gravitons are fused photons propagating in four dimensions. The model describes gravitational attraction between two bodies, each of simplified geometric…
Within the recently proposed Lorentz invariant formalism for description of neutrino spin evolution in presence of an arbitrary electromagnetic fields effects of matter motion and polarization are considered.
The motion of a local source inducing small oscillations in the gravitational field is investigated and shown to exhibit pure rotational kinetic energy. Should the net affect of these slow, revolving oscillations cause large-scale rotations…
A description of electromagnetism as four-dimensional spacetime structure leads to the dynamics of a charged particle being determined only by the four-vector potential and the existence of an electromagnetic field depending on the…
In the present work, we will derive the expression for the change in direction of the electric field using the Lorentz transformation for inertial frame or un-accelerated frame. The acceleration also influences the observed rate of a moving…
We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions $f,g$. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to…
The frequency shift of light in the gravitational field generated by a rotating body is investigated. We consider the scenario in which both the light source and the observer are in motion. The frequency shift is calculated up to the…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
In this paper the physical systems consisting of relatively moving subsystems are considered in the "true transformations relativity." It is found in a manifestly covariant way that there is a second-order electric field outside stationary…
Dynamics with noncommutative coordinates invariant under three dimensional rotations or, if time is included, under Lorentz transformations is developed. These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)…
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
By means of the rotational transformations of octonion coordinate systems, the paper aims to explore the physical properties of conserved quantities relevant to the vectorial magnitudes within the material media, revealing the simultaneity…
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…