Related papers: Characterizing Klein-Fock-Gordon-Majorana particle…
We describe a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Amp\`ere partial differential equations and first-order Lagrangians. This condition is based on comparing…
In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first…
The Proca-Corben-Schwinger equations for a spin-1 particle with an anomalous magnetic moment are added by a term describing an electric dipole moment, then they are reduced to a Hamiltonian form, and finally they are brought to the…
A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version…
The structure of the electromagnetic vertex function of spin-3/2 particles is analyzed in a general way, for the diagonal and off-diagonal couplings, of charged as well as neutral particles including the case of self-conjugate (Majorana)…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic…
Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables,…
We give the governing equations for multiple scalar fields in a flat Friedmann-Robertson-Walker (FRW) background spacetime on all scales, allowing for metric and field perturbations up to second order. We then derive the Klein-Gordon…
We solve the Klein-Gordon equation in any $D$-dimension for the scalar and vector general Hulth\'{e}n-type potentials with any $l$ by using an approximation scheme for the centrifugal potential. Nikiforov-Uvarov method is used in the…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and…
Recently there has been great interest around quantum relativistic models for plasmas. In particular striking advances have been obtained by means of the Klein-Gordon-Maxwell system, which provides a first order approach to the relativistic…
In previous works, we showed that both time and space can emerge from entanglement within a globally constrained quantum Universe, with no background coordinates. By extending the Page and Wootters quantum time formalism to include both…
We show a procedure to classically simulate the Majorana equation in 1+1 dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose a novel approach that uses a…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
A Majorana fermion is the single fermionic particle that is its own antiparticle. Its dynamics is determined by the Majorana equation where the spinor field $(\psi)$ is by definition equal to its charge-conjugate field $(\psi_c)$. Here, we…