相关论文: Rotation Representations and e, $pi$, p Masses
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
In Parts I and II we showed that e, $\nu$ propagators can be derived from rotation invariant projection operators, thereby providing examples of how quantities with spacetime symmetry can be obtained by constraining rotationally symmetric…
It is an easily deduced fact that any four-component spin 1/2 state for a massive particle is a linear combination of pairs of two-component simultaneous rotation eigenstates, where `simultaneous' means the eigenspinors of a given pair…
A novel theory of the structure of elementary particles is outlined. The proposed relativistic covariant space-time approach supposes that all massive particles are composite particles formed by massless elementary particles with opposite…
The quark masses evaluated by the Particle Data Group are consistent with terms in a geometric progression of mass values descending from the Planck Mass. The common ratio of the sequence is 2/pi. The quarks occupy the 'principal' levels of…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|^2 is 1. They occur as the phase phi(E) defined by r(E) = t*(E)/t(E) = 1e^{i 2phi(E)} undergoes a rapid change…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
Postulating that spacetime is discrete, we assume that physical space is described by a 3-dimensional cubic lattice.The corresponding symmetry group of rotations has order 24 and motivates the introduction of a cubic shaped graph with 27…
Einstein's photo-electric effect allows us to regard electromagnetic waves as massless particles. Then, how is the photon helicity translated into the electric and magnetic fields perpendicular to the direction of propagation? This is an…
The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of…
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…
The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D…
In this work we represent the $1/2$ Spin particles with complex quaternions using a transformation to 2x2 matrices in order to obtain the Pauli matrices. With this representation we determine the states, rotation operators and the total…
Rotations and poses are ubiquitous throughout many fields of science and engineering such as robotics, aerospace, computer vision and graphics. In this paper, we provide a complete characterization of rotations and poses in terms of the…
This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of…
The author discusses particular solutions of a second order equation designated by source equation. This equation is special because the metric of the space where it is written is influenced by the solution, rendering the equation…
Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie group allows to create an explicitly given Lorentz invariant fermion wave. As the generators are real valued they can be interpreted as a deformation tensor in…