Related papers: Quaternionic Electron Theory: Geometry, Algebra an…
Dirac's equations are formulated in a consistent way by using only elements from each of R, C, and H. In H, the quaternions, the symmetry resulting from a "single" conjugation (i, j, or k) results in three conserved currents - possibly…
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…
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
We present new parametrizations of elements of spinor and orthogonal groups of dimension 4 using Grassmann exterior algebra. Theory of spinor groups is an important tool in theoretical and mathematical physics namely in the Dirac equation…
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…
A study of fundamental geometrical interactions shows that the Dirac electron can be represented as a conformal wave. A Riemannian space is used, having coordinates that transform locally as spinors. The wave function becomes a gradient.…
It is set manifest an underlying algebraic structure of Dirac equation and solutions, in terms of Cl2 Clifford algebra projectors and ladder operators. From it, a scheme is proposed for constructing unified field theories by enlarging the…
We extend the biquaternionic Dirac equation to include interactions with a background bosonic field. The obtained biquaternionic Dirac equation yields Maxwell-like equations that hold for both a matter field and an electromagnetic field.…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and…
The recent literature shows a renewed interest, with various independent approaches, in the classical models for spin. Considering the possible interest of those results, at least for the electron case, we purpose in this paper to explore…
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are…
We discuss the use of the variational principle within quaternionic quantum mechanics. This is non-trivial because of the non commutative nature of quaternions. We derive the Dirac Lagrangian density corresponding to the two-component Dirac…
We present a new analysis of the connection between the classical conservation theorems and the role played by the Dirac matrices in order to obtain a four spinor version of the Dirac equation for the two electrons bound problem. The…
The Dirac equation in four time and four space dimensions (or (4+4)-dimensions) is considered. Step by step we show that such an equation admits Majorana and Weyl solutions. In order to obtain the Majorana or Weyl spinors we used a method…
We find in our quaternionic version of the electroweak theory an apparently hopeless problem: In going from complex to quaternions, the calculation of the real-valued parameters of the CKM matrix drastically changes. We aim to explain this…
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…
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.…