Related papers: A new development in quantum field equations of dy…
We address the Klein-Gordon equation for a spinless charged particle in the presence of an electromagnetic (EM) field, and focus on its known shortcoming, related to the existence of solutions with a negative probability density. We…
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…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
Expanding the ordinary Dirac's equation in quaternionic form yields Maxwell-like field equations. As in the Maxwell's formulation, the particle fields are represented by a scalar, $\psi_0$ and a vector $\vec{\psi}$. The analogy with…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This…
The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase…
The canonical quantization of $D=2n$ dimensional Dirac spinning particle in the external electromagnetic field is carried out in the gauge which allows to describe simultaneously particles and antiparticles (massive and massless) already at…
We solve Klein-Gordon equation (KGE) in the framework of the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The presented solution is the simplest ever obtained for quaternionic quantum theories, and the…
We consider non-Abelian dyons in Einstein-Yang-Mills-Higgs theory. The dyons are spherically symmetric with unit magnetic charge. For large values of the electric charge the dyons approach limiting solutions, related to the Penney solutions…
Demonstrating the split octonion formalism for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), relevant field equations are derived in compact, simpler and manifestly…
This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$ fields one has a…
Recently two methods have been developed for the quantization of the electromagnetic field in general dispersing and absorbing linear dielectrics. The first is based upon the introduction of a quantum Langevin current in Maxwell's equations…
Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated to regions bounded by them. This realizes crucial elements of the general boundary…
The Proca field describes a massive relativistic spin-$1$ particle and was originally formulated in Minkowski spacetime. Here we consider a variety of generalizations in globally hyperbolic spacetimes, including couplings between a number…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…