We calculate the Green function for the Dirac equation describing a spin 1/2 particle in the presence of a potential which is a sum of the Coulomb potential VC = −A1/r and a Lorentz scalar Vs = −A2/r. The bound state spectrum is obtained. PACS numbers:03.65.Pm,03.65.Ge ⋆ e-mail:[email protected]

Anisotropic regularization PDE’s (Partial Differential Equation) raised a strong interest in the field of image processing. The benefit of PDE-based regularization methods lies in the ability to smooth data in a nonlinear way, allowing the preservation of important image features (contours, corners or other discontinuities). In this article, we propose a PDE-based method restoration approach in...

We derive the scalar potential in zero mode effective action arising from a de Sitter brane embedded in five dimensions with bulk cosmological constant Λ. The scalar potential for a scalar field canonically normalized is given by the sum of exponential potentials. In the case of Λ = 0 and Λ > 0, we point out that the scalar potential has a unstable local maximum at the origin and exponentially ...

A quantum model of gravitation interacting with a Born-Infeld(B-I) type scalar field ϕ is considered. The corresponding Wheeler-Dewitt equation can be solved analytically for both very large and small ˙ ϕ. In the extreme limits of small cosmological scale factor the wave function of the universe can be obtained by applying the methods developed by Vilenkin, Hartle and Hawking. We also suggest t...

A quantum model of gravitation interacting with a Born-Infeld(B-I) type scalar field ϕ is considered. The corresponding Wheeler-Dewitt equation can be solved analytically for both very large and small ˙ ϕ. In the extreme limits of small cosmological scale factor the wave function of the universe can be obtained by applying the methods developed by Vilenkin, Hartle and Hawking. We also suggest t...

We establish necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrödinger operators with a positive scalar potential. They are expressed in terms of Wiener capacity and local energy of the magnetic field. These conditions depend on two functional parameters. One of them is a decreasing function of one variable whose argument is the normalize...

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eliminating the auxiliary fields only if constraints are imposed on the mass matrices utilised in the Dirac operator. Th...

We construct a scalar potential of supersymmetric left-right model in the limit when supersymmetry is valid.

Abstract: There are two possible methods for the inclusion of the chemical potential in a relativistic bosonic field theory. The most popular method has recently been criticised by some authors, so much so as to require a re-analysis of the entire problem. I here present a new approach to the inclusion of the chemical potential that uses the second method and zeta-function regularisation techni...

In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function.   The general solution of the equation of motion is obtained, which satisfies the required radiation condition.  The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for...