Bound-state,Bethe—Salpeter solutions with conjugate pairs of complex coupling constants

Solutions are obtained to the Bethe-Salpeter equation describing bound states of two massive scalars interacting via the exchange of a third, massive scalar. Covariance of the equation implies that the interaction is retarded, and in part because the energy appears more than once in the equation, a Hamiltonian for the bound state does not exist. Thus in contrast to the Schrodinger equation, the Bethe-Salpeter equation is solved by specifying the energy and solving for the coupling constant as an eigenvalue. Although the Bethe-Salpeter equation is derived from a Lagrangian with real coupling constants, depending on the value of the energy and the masses of the scalars, some values of the coupling constant that satisfy the Bethe-Salpeter equation are complex and always occur in conjugate pairs. The unexpected existence of solutions with real energy and a complex coupling constant raises the possibility that there are also resonance solutions with real values of the coupling constant and complex energy. Supported by a grant from the Ohio Supercomputer Center. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

The relativistic bound states for a new ring-shaped harmonic oscillator

In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.     

Space-Like Form of Bethe-Salpeter Equation: Bound State

According to Dirac's principle, we apply the space-like consistency conditions in a relativistic theory to two-particle system and then define the space-Like wavefunctions through introducing a space-like factor, which is equivalent to Bethe-Salpeter wavefunction in physical content. The space-like form of Bethe-Salpeter equation of bound states is derived in terms of the universal rearranging technology of interaction kernel. Its advantages are of explicit Lorentz-covariant form and the difficulty of ghost states is automatically overcome. We also discuss the normalization condition of the space-like function.     

一类环状非球谐振子势场中相对论粒子的束缚态解

提出了一种新的环状非球谐振子势, 在标量势与矢量势相等的条件下，给出了其Klein-Gordon方程和Dirac方程的束缚态解. Klein-Gordon方程的θ角向波函数以超几何函数表示，径向波函数可用合流超几何函数或广义拉盖尔多项式表示，能谱方程由径向波函数满足的束缚态边界条件得到. Dirac方程的旋量波函数可用Klein-Gordon方程的解构造. 关键词： 环状非球谐振子势 Klein-Gordon方程 Dirac方程 束缚态     

New Closed Expression of Interaction Kernel in Bethe-Salpeter Equation for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green＇s functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green＇s function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore, the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.     

New Closed Expression of Interaction Kernel in Bethe-Salpeter Equation for Quark-Antiquark Bound States

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the irreducible decomposition of the Green‘s functions involved in the Bethe-Salpeter equation satisfied by the quark-antiquark four-point Green‘s function. The interaction kernel derived is given a closed and explicit expression which shows a specific structure of the kernel since the kernel is represented in terms of the quark, antiquark and gluon propagators and some kinds of quark, antiquark and/or gluon three, four, five and six-point vertices. Therefore,the expression of the kernel is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.     

Neutron star equation of state in density dependent relativistic Hartree-Fock theory*

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M☉, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.     

Neutron star equation of state in density dependent relativistic Hartree-Fock theory

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M_⊙, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.     

Relativistic Description of Heavy Quarkonium Dissociation in Hot Matter

The mass spectrum and binding radii of heavy-quark bound states are analyzed in terms of the reduced Bethe-Salpeter equation. The critical values of screening masses for cc and bb bound states at finite temperature are obtained and compared with the previous results given by nonrelativistic models.     

Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions

We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating the corresponding topological index, we show a precise equivalence between both indices to confirm the index theorem. Finally, we apply this observation to reexamine the role of another topological invariant, i.e., the Chern number associated with the Berry curvature proposed in the study of protected zero modes along the lines of topological classification of insulators and superconductors. We show that the Chern number is equivalent to the topological index, implying that it indeed reflects the number of zero-energy states. Our theoretical model belongs to the BDI class from the viewpoint of symmetry, whereas the spatial dimension d of the system is left arbitrary throughout the paper.     

A simple derivation of the three magnon bound state equation

A simple derivation of the equation for determining the bound states of three magnons in the Heisenberg linear chain with longitudinal anisotropy is given. The present method utilizes nothing more than the Schrödinger equation and Faddeev’s three body equations, and avoids the introduction of the ideal spin wave Hilbert space.     

Heavy-light mesons in a relativistic model

We study the heavy-light mesons in a relativistic model, which is derived from the Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation to the heavy quark. The kernel we choose is based on scalar confinement and vector Coulomb potentials. The transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of D, D_s, B, B_s meson states are obtained. The spectra are calculated up to the order of 1/m Q, and wave functions are treated to leading order.     

无反射势阱中相对论粒子的束缚态

给出了具有无反射势型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 关键词： 无反射势 Klein-Gordon方程 Dirac方程 束缚态     

Rosen-Morse势阱中相对论粒子的束缚态

给出了具有Rosen-Morse型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 运用超对称量子力学和形不变性得到了束缚态能谱，通过变量代换求得波函数. 把上述方法推广到相对论量子力学. 关键词： Rosen-Morse势 Klein-Gordon方程 Dirac方程 束缚态     

第二类Poeschl-Teller势场中相对论粒子的束缚态

给出了具有第二类Poeschl—Teller型标量势与矢量势的Klein-Gordon方程和Dirac方程的8波束缚态解，其解可用超几何函数表示．     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

相对论情况下赝自旋对称性势场中运动粒子的束缚态

在赝自旋对称性条件下,分别求解了在M rse型和Tan2(πηr)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.     

相对论类空方程

根据Dirac类空自洽性条件的思想,通过引入类空因子定义了类空波函数.它的物理部分与Bethe-Salpeter波函数相一致.利用普适的相互作用核的重排技术,导出了对于束缚态和散射态的相对论类空方程,并且将它们推广到多粒子的情形.也得到了束缚态类空波函数的归一化条件和散射态类空方程的非齐次项的解.因此,建立起了相对论类空方程体系.     

相对论质量修正效应对超高次谐波的影响

通过分别求解含时狄拉克方程和含时薛定谔方程, 研究了一维模型原子在相对论超强激光脉冲作用下的超高次谐波发射过程. 研究结果表明: 在弱场强条件下, 相对论的模拟结果可以退化到非相对论的结果; 随着场强的增强, 可以逐渐观察到明显的相对论质量修正效应. 此外, 根据发展的相对论的"三步"模型并结合小波时频分析方法, 分析了谐波平台的截止位置和发射效率.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.