Related papers: The Dirac-Hestenes Equation for Spherical Symmetri…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
Recently Daviau showed the equivalence of ordinary matrix based Dirac theory -formulated within a spinor bundle S_x \simeq C^4_x-, to a Clifford algebraic formulation within space Clifford algebra CL(R^3,delta) \simeq M_2(C) \simeq P \simeq…
Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group $\mathrm{SO}(3)$. The aim of this work is to make use of this tool also…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend…
The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. The spin and pseudospin symmetry…
The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our…
The construction of Dirac observables, that is gauge invariant objects, in General Relativity is technically more complicated than in other gauge theories such as the standard model due to its more complicated gauge group which is closely…
We present a general formalism based on the framework of non-commutative geometry, suitable to the study the standard model of electroweak interactions, as well as that of more general gauge theories. Left- and right-handed chiral fields…
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…
We examine the bound state solutions of the Dirac equation under the spin and pseudospin symmetries for a new suggested combined potential, Hulten plus a class of Yukawa potential including a Coulomb-like tensor interaction. An improved…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…
In this paper, we consider the Cauchy problem of Dirac equations with Chern-Simons-Proca (CSP) gauge field. We investigate global well-posedness and scattering theory for the solutions with small initial data. The main difficulties come…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
Solutions of the Dirac equation with spin and pseudospin symmetry for the scalar and vector trigonometric scarf potential in $D$-dimensions within the framework of an approximation scheme to the centrifugal barrier are obtained. The energy…
In this paper, we investigate the Dirac equation with the Killingbeck potential under the external magnetic field in non-commutative space. Corresponding to the expressions of the energy level and wave functions in spin symmetry limit and…
We have recently shown that the space of initial data (covariant phase space) of the relativistic oscillator in Minkowski space $\mathbb{R}^{3,1}$ is a homogeneous K\"ahler-Einstein manifold $Z_6$=AdS$_7$/U(1)=U(3,1)/U(3)$\times$U(1). It…
We find the exact bound-state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulth\'{e}n potential in the case where we have a particular mass function…
Embedding of Klein-Gordon and Dirac particle onto Riemannian submanifold in higher dimensional Minkowski space is given by using Hamiltonian BRST formalism. Up to the ordering and quantum potential term induced by embedding, obtained K-G…
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie…