Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials

We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity conditions are discussed. As an application, we consider a pseudoscalar Dirac potential related to the Schrödinger model for the rationally extended radial oscillator. The pseudoscalar partner potentials are constructed under the first- and second-order Darboux transformations.     

Dirac equation with vector and scalar cornell potentials and an external magnetic field

The two‐dimensional Dirac equation in the presence of vector and scalar Cornell potentials as well as an external magnetic field by a quasiexact methodology are investigated. The closed form of the eigenfunctions is reported and the energy behavior for different states is numerically discussed.     

On geometric quantization of the Dirac magnetic monopole

We give a simple derivation of the spectrum of the Dirac magnetic monopole on a unit sphere S² based on geometric quantization and the Frobenius reciprocity formula. The starting point is the calculation by Novikov and Schmelzer of the canonical symplectic structure on the coadjoint orbits of the isometry group of 3-dimensional Euclidean space E(3), which showed the appearance of the Dirac magnetic term.     

Nambu-Jona-Lasinio version of magnetic monopole physics with dual Dirac strings

We propose a model where a condensate of monopole-antimonopole pairs leads to confinement. Magnetic monopoles are considered as massless fermion fields interacting via local four-monopole interaction of the Nambu-Jona-Lasinio kind leading to monopole condensation. Condensation of magnetic monopole currents and any derivative of them are obtained. It is shown that the bosonized version of this Monopole Nambu-Jona- Lasinio (MNJL) model is reducing to London’s theory of dual superconductivity within Dirac’s extension of Maxwell’s Electrodynamics. The affinity of the MNJL-model with Compact Quantum Electrodynamics is discussed.     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

Superspace formulation of the dynamical symmetries of the Dirac magnetic monopole

The superspace formulation for the dynamical supersymmetry of the Pauli system in the presence of a Dirac magnetic monopole is presented. It is used to prove that Osp(1, 1) is the largest dynamical invariance group of this system. The action of finite transformations on the parameters of superspace and on the supervariables is given.     

On integrable rational potentials of the Dirac equation

The one-dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the results have to be stated with recursive relations, because in general the equation is of Heun type. The inverse problem of finding integrable rational potentials based on the properties of the singular points is also presented; in particular, a general class of integrable potentials leading to the Whittaker equation is found.     

Solution of the Dirac equation in quaternions

A technique is considered for solving in quaternions the Dirac equation for particles with an anomalous magnetic moment in the field of a plane electromagnetic wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 43–46, October, 1981.     

Wave equation for a magnetic monopole

We show that there is room, in the Dirac equation, for a massless monopole. The basic idea is that the Dirac equation admits a second electromagnetic minimal coupling associated to the chiral gauge , which is only valid for a massless particle, but satisfies all the symmetry laws of a monopole. In the problem of the diffusion on a central electric field, we find the Poincaré integral and the Dirac relationeg/=n/2. The latter is deduced as a consequence of the fact (which is shown in this paper) thateg/c is the projection of the total angular momentum on the symmetry axis of the system formed by the monopole and the electric charge. Another important property is that a monopole and an antimonopole have opposite helicities (as for the neutrino), but do not have opposite charges: this precludes a vacuum magnetic polarization which would be analogous to the electric one, but allows us to imagine an aether made up of monopole-antimonopole pairs. The theory is then generalized on the basis of a nonlinear equation which is the most general invariant equation under the chiral gauge law. This equation admits solutions corresponding to massive monopoles, among which there are bradyons (i.e., ordinary massive particles) and tachyons. This equation is shown to be closely related to previous works initiated by Hermann Weyl, on Dirac's theory in the framework of general relativity. In conclusion, it is suggested that massless monopoles are perhaps excited states of the neutrino and that they may be produced in some weak interactions. Consequences on the solar activity are considered.     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

Manning-Rosen标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Manning-Rosen型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态解，其解可用超几何函数表示. 关键词： Manning-Rosen势 Klein-Gordon方程 Dirac方程 束缚态     

Dirac magnetic monopole production from photon fusion in proton collisions

We calculate the lowest-order cross-section for Dirac magnetic monopole production from photon fusion ( in p collisions at = 1.96 TeV, pp collisions at = 14 TeV, and we compare with Drell-Yan (DY) production. We find the total cross-section is comparable with DY at = 1.96 TeV and dominates DY by a factor > 50 at = 14 TeV. We conclude that both the and DY processes allow for a monopole mass limit m > 370 GeV based upon the null results of the recent monopole search at the Collider Detector at Fermilab (CDF). We also conclude that production is the leading mechanism to be considered for direct monopole searches at the Large Hadron Collider (LHC).     

The WKB method for the Dirac equation with the vector and scalar potentials

The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated. Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done.     

具有一维Coulomb型对称势Dirac方程的精确解

在标量势大于矢量势的情况下,一维Dirac方程的束缚态能级是二重简并的.任意两个不同能量本征值的波函数和同一能量本征值的两个波函数都是相互正交的.对于纯标量场,存在零能量束缚态,存在分数电荷 关键词： Coulomb型对称势 Dirac方程 束缚态 分数电荷     

Invariance properties of the Dirac monopole

The quantum mechanical motion of a spinless electron in the external field of a magnetic monopole of magnetic charge μ is investigated. It is shown that Dirac's quantum condition $\text{2μe(}\text{h}\text{?}\text{c)}{}^{\mathrm{?1}}\text{= n}$ for the string being unobservable ensures rotation invariance and correct space reflection properties for any integer value of n. The rotation and space reflection operators are found and their group theoretical properties are discussed. When n is odd, half-integer j representations of the SU(2) group emerge without the introduction of spin. A method for constructing conserved quantities in the case when the potential is not explicitly invariant under the symmetry operation is also presented and applied to the discussion of the angular momentum of the electron-monopole system.     

Dirac equation with scalar and vector quadratic potentials and Coulomb-like tensor potential

It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed.     

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization condition are analyzed. In addition, a misconception diffused in the literature on the interaction of neutral fermions is clarified.     

具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的束缚态

给出了具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解.     

Dirac equation exact solutions for generalized asymmetrical Hartmann potentials

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 potential. The cases of some quasi-exactly solvable and Morse-like potentials are briefly commented.