Related papers: Characterizing Klein-Fock-Gordon-Majorana particle…
We are interested in the Klein-Gordon-Zakharov system in $\mathbb{R}^{1+2}$, which is an important model in plasma physics with extensive mathematical studies. The system can be regarded as semilinear coupled wave and Klein-Gordon equations…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…
We present a systematic theoretical framework for investigating first-order electromagnetic (EM) perturbations induced by gravitational waves (GWs). Beginning with the covariant Maxwell equations, we derive the complete first-order…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
We solve the one-dimensional time-independent Klein-Gordon equation in presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker $M_{\kappa,\mu}(x)$ function, and the antiparticle bound state is…
Let $G$ be a compact Lie group. In this article, we consider the initial value fractional wave equation with power-type nonlinearity on $G$. Mainly, we investigate some $L^{2}-L^{2}$ estimates of the solutions to the homogeneous fractional…
We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic…
The Maxwell-Klein-Gordon equations in 2+1 dimensions in temporal gauge are locally well-posed for low regularity data even below energy level. The corresponding (3+1)-dimensional case was considered by Yuan. Fundamental for the proof is a…
Here, we consider a classically scale-invariant extension of the Standard Model (SM) with two-component dark matter (DM) candidates, including a Dirac spinor and a scalar DM. We probe the parameter space of the model, constrained by relic…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the correct Schrodinger equation in the low-speed limit, is presented. Under this theoretical framework, that affords an interpretation of the quantum potential, the main…
We prove global in time dispersion for the wave and the Klein-Gordon equation inside the Friedlander domain by taking full advantage of the space-time localization of caustics and a precise estimate of the number of waves that may cross at…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
The generalized Dirac equation of the third order, describing particles with spin 1/2 and three mass states, is analyzed. We obtain the first order generalized Dirac equation in the 24-dimensional matrix form. The mass and spin projection…
Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime and a uniform magnetic field are studied in the context of the so called, metaphorically speaking, position-dependent mass (PDM) settings. We show that the corresponding…
For the $1+1$ dimensional nonlinear damped stochastic Klein-Gordon equation driven by space-time white noise, we prove that the second-order increments of the solution can be approximated, after scaling with the diffusion coefficient, by…
First-order phase transitions exist in many models beyond the Standard Model and can generate detectable stochastic gravitational waves for a strong one. Using the cosmological observables in big bang nucleosynthesis and cosmic microwave…
We consider the Klein-Gordon equation in FRW-like spacetimes, with compact space sections (not necessarily isotropic neither homogeneous). The bi-scalar kernel allowing to select the positive-frequency part of any solution is developed on…
It has recently been shown that the classical electric and magnetic fields which satisfy the source-free Maxwell equations can be linearly mapped into the real and imaginary parts of a transverse-vector wave function which in consequence…
To Milne's Lorentz-group-based spacetime and Gelfand-Naimark unitary representations of this group we associate a Fock space of 'cosmological preons'-quantum-theoretic universe constituents. Milne's 'cosmological principle' relies on…