Related papers: Negative Energy Solutions and Symmetries
A negative symmetry is a nonlocal symmetry of special type. In this paper, we introduce a method for constructing negative symmetries from consistent triplets of differential and differential-difference equations. Moreover, we study the…
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of vector and scalar generalized Hartmann potentials. This is done provided the vector potential is equal to or minus the scalar…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
The Dirac equation is generalized to $D+1$ space-time.The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd $D$ and even $D$ cases. The…
We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries, i.e., when those potentials have the same magnitude and either the…
We present a supersymmetric model of dark energy from Mass Varying Neutrinos which is stable against radiative corrections to masses and couplings, and free of dynamical instabilities. This is the only such model of dark energy involving…
In this paper, a theory of dark energy is proposed that matches dark matter. The relativistic quantum mechanics equations reveal that free particles can have negative energies. We think that the negative energy is the dark energy which…
Dirac equation for the finite dipole potential is solved by the method of the join of the asymptotics. The formulas for the near continuum state energy term of a relativistic electron-dipole system are obtained analytically. Two cases are…
In this article we consider the question of the existence of positive symmetric solutions to the problems of the following type $\Delta u=a\left( \left\vert x\right\vert \right) h\left( u\right) +b\left( \left\vert x\right\vert \right)…
We study the asymptotic behaviour of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of…
We analyze the Lagrangian density and canonical stress-energy tensor for the Dirac equation, where the Dirac bispinor has been recast as a multivector set of fields. For the massless Dirac field, the sign of the energy density is determined…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
The problem of dark energy is briefly reviewed in both theoretical and observational aspects. In the theoretical aspect, dark energy scenarios are classified into symmetry, anthropic principle, tuning mechanism, modified gravity, quantum…
A general energy dispersion relation is developed for metamaterials having the negative-refraction (NR) property. It is shown that absorption effects are involved with NR phenomena, and the conditions under which NR occurs are discussed.…
Using different parameterizations of the nuclear mass formula, we study the sensitivity of the isoscaling parameters to the mass formula employed in grand-canonical calculations. Previous works on isoscaling have suggested that the symmetry…
A study of the correlation between nuclear temperatures and symmetry energy is presented for heavy-ion collisions at intermediate energies via the isospin-dependent quantum molecular-dynamics model. It is found that different symmetry…
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic…
Higher dimensional super symmetry has been analyzed in terms of quaternion variables and the theory of quaternion harmonic oscillator has been analyzed. Supersymmertization of quaternion Dirac equation has been developed for…
Recent successes in {\it ab initio} calculations of light nuclei (A=2-6) will be reviewed and correlated with the dynamical consequences of chiral symmetry. The tractability of nuclear physics evinced by these results is evidence for that…