Related papers: Coordinate transformations in quaternion spaces
Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the universe by different geometries. Field transformations for functional flow equations…
Modifications of a free quantum field calculation using translation-related concepts and general translation representations yield quantum fields for massive particles that as a consequence follow the classical trajectories of…
A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenboeck connection. In a tetrad…
Based on Maxwellian quaternionic electromagnetic theory, the electromagnetic interaction, gravitational interaction and their coupling influence with the dark matter field in octonionic space are discussed. The research results disclose the…
Following a previous proposition of quaternity spacetime for electronic orbitals in neon shell, this paper describes the geometrical course each electron takes as it oscillates harmonically within a certain quaternity space dimension and…
We consider the conversion of gravitons and photons as a four-wave mixing process. A nonlinear coupled systems of equations involving two gravitons and two photons is obtained, and the energy exchange between the different degrees of…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
We consider the transformation for the point rotation frames with the angle, spatial coordinate along the axis of rotation and time as variables. The problem arises when light, propagating through 3-fold electrooptical crystal, is modulated…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…
We analyze the transformation of quantum fields under conformal coordinate transformations from inertial to accelerated frames, in the simple case of scalar massless fields in a two-dimensional spacetime, through the transformation of…
Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…
Transformation rules for coordinates, velocities and accelerations in accelerated reference frames are derived. A generalized approach of the special relativity is taken for a basis. A 7-dimensional space including projections of velocity…
Many candidate fundamental theories contain scalar fields that can acquire spacetime-varying expectation values in a cosmological context. Such scalars typically obey Lorentz-violating effective dispersion relations. We illustrate this fact…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
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…
In the space and the time with a fractional dimensions the Lorents transformations fulfill only as a good approach and become exact only when dimensions are integer. So the principle of relativity (it is exact when dimensions are integer)…
Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…
Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division…