Related papers: Dirac equation and its squared form
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
For a differential equation with interaction, we investigate its ergodic properties. We apply the obtained results to study the limiting behavior of braid invariants associated with the flow of solutions.
This article discusses some important applications of the quadratic function with the aim of highlighting the importance of cuadr\'aticas.- forms are also intended to show how a simple function covers virtually all areas of knowledge are…
The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…
A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the…
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…
We apply Dirac's square root idea to constraints for embedded 4-geometries swept by a 3-dimensional membrane. The resulting Dirac-like equation is then analyzed for general coordinates as well as for the case of a Friedmann-Robertson-Walker…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
We show that additional solutions must be ignored (in differences of the Schrodinger and Klein-Gordon equations) in the Dirac equation, where usually passed the second order radial equation, called the reduced equation, instead of a system.…
It is shown that the known method to solve the Dirac equation by means of the squaring method, when relying on the scalar function of the form \Phi = e^{-i\epsilon t} e^{ik_{1} x} e^{ik_{2} y} \sin (kz + \alpha) leads to a 4-dimensional…
An analytical solution of the Dirac equation with a Cornell potential, with identical scalar and vectorial parts, is presented. The solution is obtained by using the linear potential solution, related to Airy functions, multiplied by…
We study $(2+1)$ dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another…
Motivated by examples obtained from conformal deformations of spectral triples and a spectral triple construction on quantum cones we propose a new twisted reality condition for the Dirac operator.
The intertwining technique has been widely used to study the Schr\"odinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of…
A general procedure of local reduction for the Dirac equation is introduced to study one- and n-body interacting systems. In the one-body case we show that the reduction allows for an approximate solution of the Dirac equation, correlating…
Due to some current interest in this subject we have produced this note. There is no claim to anything new, except possibly to show that a direct numerical approach is quite simple and instructive. For comparison purposes we include a…
In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and the…
A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ -- D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free…
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…