相关论文: Recoil Correction in the Dirac-Coulomb Problem
A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part…
Coulomb gauge QCD in the first order formalism can be written in terms of a ghost-free, nonlocal action that ensures total color charge conservation via Gauss' law. Making an Ansatz whereby the nonlocal term (the Coulomb kernel) is replaced…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
Numerical results for the first gap of the Lyapunov spectrum of the self-dual random-bond Ising model on strips are analysed. It is shown that finite-width corrections can be fitted very well by an inverse logarithmic form, predicted to…
We consider the constraints on the effective Lagrangian of the rank-one gauge field on D-branes imposed by the equivalence between the description by ordinary gauge theory and that by non-commutative gauge theory in the presence of a…
We show that one of exact solutions of the second-order Dirac-Coulomb equation were pseudo. In the corresponding original literature, it was considered that the mass of the electron with a Coulomb potential was position-dependent, but the…
We study the consistency of the non-Abelian Coulomb gauge. There are energy divergences in individual diagrams, which are known to cancel at 2-loop order when suitable sets of diagrams are summed. We investigate to 3-loop order the…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
We consider the following inverse problem: Suppose a $(1+1)$-dimensional wave equation on $\mathbb{R}_+$ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
We establish simple connections between response functions of the dynamical Dirac systems and $A$-amplitudes and Weyl functions of the spectral Dirac systems. Using these connections we propose a new and rigorous procedure to recover a…
In this article we study the problem of recovering the initial data of the two-dimensional wave equation from Neumann measurements on a convex domain with smooth boundary in the plane. We derive an explicit inversion formula of a so-called…
We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic…
We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's $K$ operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases.…
A representation of solutions of the one-dimensional Dirac equation is obtained. The solutions are represented as Neumann series of Bessel functions. The representations are shown to be uniformly convergent with respect to the spectral…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Dirac equation. To this end we develop basic scattering theory and establish a limiting absorption principle for discrete perturbed Dirac operators.
Starting with the Dirac equation for an electron in a constant electromagnetic background on a noncommutative (NC) plane, we obtain a gauge invariant description of the system. Surprisingly, the dynamics of the system is dictated by the…
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…
The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting…