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Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
The kinematical formalism for describing spinning particles developped by the author is based upon the idea that an elementary particle is a physical system with no excited states. It can be annihilated by the interaction with its…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
Stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product at small values of gravitational…
The spinorial degrees of freedom of two spacelike separated Dirac particles are considered and a collection of nine locally Lorentz covariant bitensors is constructed. Four of these bitensors have been previously described in [Phys. Rev. A…
Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos are to have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner's little…
From the 16-component Dirac-K\"{a}hler field theory, spinor equations for two types of massless vector photon fields with different parities have been derived. Their equivalent tensor equations in terms of the strength tensor $F_{ab}$ and…
We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This…
We present a microresonator-based system capable of simultaneously producing time-advanced and time-delayed pulses. The effect is based on the combination of a sharp spectral feature with two orthogonally-polarized propagating waveguide…
We analyse quantised scalar, spinor and photon fields in a mechanically rigid cavity that is accelerated in Minkowski spacetime, in a recently-introduced perturbative small acceleration formalism that allows the velocities to become…
Topological semimetals, representing a new topological phase that lacks a full bandgap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a…
As an interpretation of the 750 GeV diphoton excesses recently reported by both ATLAS and CMS collaborations, we consider a simple extension of the Standard Model with a Dirac fermion dark matter where a singlet complex scalar field…
We discuss the quasi 1-D scattering of two counter-propagating, dark-state polaritons (DSP), each containing a single excitation. DSPs are formed from photons in media with electromagnetically induced transparency and are associated with…
Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black…
We describe an experimental system that allows one to easily access the dispersion curve of exciton-polaritons in a microcavity. Our approach is based on two spatial light modulators (SLM), one for changing the excitation angles (momenta),…
Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon-Dirac equations. The introduction of a boson-fermion interaction allows a scalar vortex to act as a harmonic trap that can confine massive…
We propose a new and compact realization of singlet Dirac dark matter within the WIMP framework. Our model replaces the standard $Z_2$ stabilizing symmetry with a $Z_6$, and uses spontaneous symmetry breaking to generate the dark matter…
The couplings of the Standard Model sector to the scale invariant degrees of freedom can open the possibility to study dark photons (DP). The Dalitz-like decay of the (Higgs-like) scalar boson into a single photon and DP is studied. The…
In the presence of spin-orbit coupling (SOC), achieving both spin and valley polarized Dirac state is significant to promote the fantastic integration of Dirac physics, spintronics and valleytronics. Based on ab initio calculations, here we…
Unpinned Dirac points (DPs) are nodal point degeneracies that occur at generic momentum points lacking high symmetry, often exhibiting characteristics typically forbidden by symmetry. While this phenomenon has been observed in solid-state…