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Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
The Klein-Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, $V_{v}=V_{s} + \mathrm{const.}$ These isospectral problems are solved in a case of squared trigonometric potential…
We study the degeneracy of the energy levels of the Schroedinger equation with Kepler-Coulomb potential and of the Klein-Gordon equation on Riemannian coverings of the Euclidean space and of the Schwarzschild space-time respectively.…
The interest in the Klein-Gordon equation with different potentials has increased in recent years due to its possible applications in Cosmology, Hadron Physics and High-Energy Physics. In this work we investigate the solutions of the…
We use two correlated metric functions and transform/deform the pointlike global monopole (PGM) spacetime metric into a quasi-PGM (QPGM) spacetime one. We study Klein-Gordon (KG) particles (manifestly introduced by the non-minimal coupling…
The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
We investigate the vacuum polarization effects associated with a charged massless spin-1/2 field in a higher-dimensional space-time, induced by a composite topological defect. The defect is constituted by a global monopole living on a…
The cosmological constant problem is examined under the assumption that the extrinsic curvature of the space-time contributes to the vacuum. A compensation mechanism based on a variable cosmological term is proposed. Under a suitable…
We point out incorrect equations derived in a paper published in this journal Ref. [1] (E. O. Silva, Eur. Phys. J. Plus (2018) 133 : 530) for the Klein-Gordon equation with the Aharonov-Bohm and Coulomb potentials in a G\"{o}del-type…
We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular…
We study the problem of two particles with Coulomb repulsion in a two-dimensional disordered potential in the presence of a magnetic field. For the regime, when without interaction all states are well localized, it is shown that above a…
Starting from a continuum theory of defects, that is the analogous to three-dimensional Einstein-Cartan-Sciama-Kibble gravity, we consider a charged particle with spin 1/2 propagating in a uniform magnetic field coincident with a wedge…
We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
Consider a conical singular space $X=C(Y)=(0,\infty)_r\times Y$ with the metric $g=\mathrm{d}r^2+r^2h$, where the cross section $Y$ is a compact $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the Klein-Gordon equations…
It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden $sl_2$-algebraic structure being one of recently-discovered quasi-exactly-solvable…
The relativistic quantum dynamics of the generalized Klein-Gordon (KG) oscillator having position-dependent mass in the G\"{o}del-type space-time is investigated. We have presented the generalized KG oscillator in this space-time, and…
We study the Klein-Gordon equation for Coulomb potential, V(r)=(-Ze^{2})/r, in quantum mechanics with a minimal length. The zero energy solution is obtained analytically in momentum space in terms of Heun's functions. The asymptotic…
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-model with cosmological constant. The $\sigma$-model can be perceived as exterior configuration of a spontaneously-broken $SO(D-1)$ global…