Related papers: The Scott correction in Dirac-Fock theory
We define the model of hydrogen atom for twist-deformed acceleration-enlarged Newton-Hooke space-time. Further, using time-dependent perturbation theory, we find in first step of iteration procedure the solution of corresponding…
We develop locale theory constructively and predicatively in univalent foundations (UF), with a particular focus on the theory of spectral and Stone locales. In the context of UF, predicativity refers specifically to the development of…
We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…
In this work we study modifications in the Aharonov-Bohm effect for relativistic spin 1/2 particles due to the noncommutativity of spacetime in $2 + 1$ dimensions. The noncommutativity gives rise to a correction to the Aharonov-Bohm…
We derive the non-retarded energy shift of a neutral atom for two different geometries. For an atom close to a cylindrical wire we find an integral representation for the energy shift, give asymptotic expressions, and interpolate…
Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties of exact Kohn-Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays…
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In…
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…
We review some peculiar features of Sudakov expansions in the calculation of electroweak radiative corrections in the MSSM at high energy. We give specific examples and consider in particular the process b g -> t W of single top quark…
The equations of the conformal field theory of gravitation with the Dirac's scalar field in Weyl-Cartan spacetime have been received. Exact solutions for Dirac's scalar field for an early Universe have been derived. Intensive decrease of…
An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of…
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry…
For a two-dimensional quantum mechanical problem, we obtain a generalized power-series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similarly to the standard effective range…
In this article, after introducing a kind of q-deformation in quantum mechanics, first, q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then three important scat erring problem in physics are studied. All…