Related papers: Coordinate transformations in quaternion spaces
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion…
Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
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 paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
We present a transformation between the Schwarzschild coordinates and local inertial coordinates, and demonstrate the effect of gravitational bending of light near a massive body in a small region. When a photon is emitted from a point near…
The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the…
Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat spacetime due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived,…
Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and…
Graviton-photon conversions in a given external electric or magnetic field, known as the Gertsenshtein mechanism, are usually treated using the four-potential for photons. In terms of the electric and magnetic (EM) fields, however, proper…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and…
We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic…
Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…
The classical processes: the conversion of photons into gravitons in the static electromagnetic fields are considered by using Feynman perturbation techniques. The differential cross sections are presented for the conversion in the electric…