Related papers: Quaternion Electromagnetism and the Relation with …
We show that all spin groups of non-definite, quinary quadratic forms over a field with characteristic 0 can be represented as 2 by 2 matrices with entries in an associated quaternion algebra. Over local and global fields, we further study…
Postulating the existence of magnetic monopole in electromagnetism and Heavisidian monopoles in gravitational interactions, a unified theory of gravi-electromagnetism has been developed on generalizing the Schwinger-Zwanziger formulation of…
Second order circularity, also called properness, for complex random variables is a well known and studied concept. In the case of quaternion random variables, some extensions have been proposed, leading to applications in quaternion signal…
M\"obius transformations of the extended complex plane are at the crossroads of many interesting topics, e.g., they form a group under composition, are the simplest form of rational function, and are a path to Lie theory. Quaternionic…
It is shown that relative coordinate and momentum of coherent electron pair have the meaning of observables with the help of quadrupole and magnetic moments. Distributions of quadrupole terms of scalar potential are shown. These…
In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…
We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop…
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 notion of the spin is shown to have two constituents, as exemplified by the spin of the electron. The first one is related to the form of the wave equation and determines the fermion or boson particle type. This implies the spin taking…
We show that Dirac 4-spinors admit an entirely equivalent formulation in terms of 2-spinors defined over the split-quaternions. In this formalism, a Lorentz transformation is represented as a $2 \times 2$ unitary matrix over the…
As previously shown, the special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz boosts and rotations. This insight indicate that the…
A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and Cayley$-$Klein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained.…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
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…
Because spatio-temporal tensors are associated with the Lorentz group, whereas spinors are associated with its covering group SL(2, C), one can associate with every tensor a spinor (but not vice versa). In particular, the (1,0)+(0,1)…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…
Dirac's equation of the electron will be discussed by using quaternions as the basis of a new formalism which seems to be very well adapted to the problem. The transformation properties of the equations as well as the invariant and…
We present a quaternion inspired formalism specifically developed to evaluate the intensity of the electrical current that traverses a single molecule connected to two semi-infinite electrodes as the applied external bias is varied. The…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…