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A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The…
In this talk we consider the geometrical basis for the reduction of the relativistic 2-body problem, much like the non-relativistic one, to describing the motion of an effective particle in an external field. It is shown that this…
The relativistic problem of spinless particle subject to a Kratzer potential is analyzed. Bound state solutions for the s-wave are found by separating the Klein-Gordon equation in two parts, unlike the similar works in the literature, which…
We investigate the propagation of electromagnetic fields and potentials in the plasma of the early Universe, assuming a Friedmann-Robertson-Walker background with negative curvature. Taking over results from classical plasma physics, we…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We notice an analogy between the motion of a relativistic particle with external homogeneous and time-dependent electromagnetic fields and the Dik'ii-Eilenberger equation for the Bogoliubov-de Gennes equation. By means of the integrable…
Relativistic effects affect nearly all notions of quantum information theory. The vacuum behaves as a noisy channel, even if the detectors are perfect. The standard definition of a reduced density matrix fails for photon polarization…
We consider superfluidity and quantum vorticity in rotating spacetimes. The system is described by a complex scalar satisfying a nonlinear Klein-Gordon equation. Rotation terms are identified and found to lead to the transfer of angular…
This paper proves that it is possible to build a Lagrangian for quantum electrodynamics which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. Gauge independence is achieved upon…
Transport properties of degenerate relativistic electrons along quantizing magnetic fields in neutron star crusts are considered. A kinetic equation is derived for the spin polarization density matrix of electrons. Its solution does not…
The problem of reduction of the wave packet of a relativistic charged particle by emission of a photon is studied with help of the path integral approach. A general expression for arbitrary order correlation function of the electromagnetic…
We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local…
The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
We investigate the relativistic generalization of the classical St\"{o}rmer problem, which describes the motion of charged particles in a purely magnetic dipole field. By incorporating special relativistic effects, the particle dynamics is…
Given the high-precision modern space mission, a precise relativistic modeling of observations is required. By solving the eikonal equation with the post-Newtonian approximation, the light propagation is determined by the iterative method…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
The radial part of the Klein-Gordon equation for the generalized Woods-Saxon potential is solved by using the Nikiforov-Uvarov method in the case of spatially dependent mass within the new approximation scheme to the centrifugal potential…
The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an $\ell^1 \mapsto \ell^\infty$ dispersive bound with polynomial decay rate $|t|^{-3/4}$. We determine the shape of the light cone for any choice of the mass…
Using the nonrelativistic approximation in the curved-space Dirac equation, the analog of the Pauli equation is derived for a weak gravitational field with a gauge fixing condition related to the synchronous gauge, in the presence of an…