Related papers: Angular momentum and torque described with the com…
In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
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.…
An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic…
The Hamiltonian formulation of the teleparallel equivalent of general relativity without gauge fixing has recently been established in terms of the Hamiltonian constraint and a set of six primary constraints. Altogether, they constitute a…
We review the concept and definitions of the energy-momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR). The importance of these definitions is justified by three major…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
We extend vector formalism by including it in the algebra of split octonions, which we treat as the universal algebra to describe physical signals. The new geometrical interpretation of the products of octonionic basis units is presented.…
Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…
A phenomenological Lagrangian approach is employed to study the electromagnetic properties of the deuteron. The deuteron is regarded as a weakly bound state of the proton and neutron. We construct a general form for the electromagnetic one-…
Defining the electric and magnetic field vectors in curved spacetime requires a proper choice of the observer's frame four-vector. Related literature shows that this fundamental issue in physics still needs to be properly resolved. In…
The 32-dimensional compounding fields and their quantum interplays in the trigintaduonion space can be presented by analogy with octonion and sedenion electromagnetic, gravitational, strong and weak interactions. In the trigintaduonion…
The expression of a time-dependent cosmological constant $\lambda \propto 1/t^2$ is interpreted as the energy density of a special type of the quaternionic field. The Lorenz-like force acting on the moving body in the presence of this…
The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell's electromagnetic equations. On…
We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
We first investigate the form the General Relativity Theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence…
We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an "orbital" and "spin" nature. All three expressions are different and it appears, on the basis of classical…
In this paper, we point out that the 4-vector force acting on a particle is always in the direction orthogonal to the 4-vector velocity of the particle in the 4-dimensional space-time, rather than along the line joining the particle and the…