Related papers: On the Dirac equation for a quark
We consider the behavior of the particles at ultra relativistic energies, for both the Klein-Gordon and Dirac equations. We observe that the usual description is valid for energies such that we are outside the particle's Compton wavelength.…
We make a review of the different works of Quark Model which are based on Perturbation theory. We make a critical analysis of taking linear part of the Potential as perturbation with Coulombic part as parent and its reverse case. We find in…
In this Chapter QCD interactions between a quark and an anti-quark are discussed. In the heavy quark limit these potentials can be related to quarkonia and $1/m$ corrections can be systematically determined. Excitations of the ground state…
Dynamical chiral symmetry breaking is described within the linear sigma model of QCD coupled to quarks. The main technical tool used for this intrinsically non--perturbative problem is an exact renormalization group equation for the quantum…
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to…
A single fermion is bound by a softcore central Coulomb potential V(r) = -v/(r^q + b^q)^(1/q), v>0, b>0, q \ge 1, in d>1 spatial dimensions. Envelope theory is used to construct analytic lower bounds for the discrete Dirac energy spectrum.…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any…
It is shown that the Dirac sea can be uniquely defined for the Dirac equation with general interaction, if we impose a causality condition on the Dirac sea. We derive an explicit formula for the Dirac sea in terms of a power series in the…
A peculiar representation of the Lorentz group is suggested as a starting point for a consistent approach to relativistic quantum theory.
In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators…
Overwhelming experimental evidence for quarks as real physical constituents of hadrons along with the QCD analogs of the Balmer Formula, Bohr Atom and Schroedinger Equation already existed in 1966. A model of colored quarks interacting with…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
We develop a relativistic free wave equation on the complexified quaternions, linear in the derivatives. Even if the wave functions are only one-component, we show that four independent solutions, corresponding to those of the Dirac…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
I briefly review a systematic approximation scheme of QCD in which the quark model picture of hadrons emerges at lowest order. A linear A^0 potential arises if Gauss' law is solved with a non-vanishing boundary condition at spatial…
The hypercentral CQM, which is inspired by Lattice QCD calculations for quark-antiquark potentials, is presented, stressing its underlying symmetry. Its results for the spectrum, the helicity amplitudes and the elastic form factors are…