约束动力学二体Dirac方程中库仑型势的奇异结构
Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
摘要：
本文利用狄拉克相对论约束动力学的两体狄拉克方程（TBDE）成功地得到了QED和QCD束缚态的协变非微扰描述。在这些应用中，库仑型势在其他方法中天真地导致在短距离处的奇异相对论修正，这需要引入微扰处理或平滑参数。我们研究了相应的奇异结构的相对论薛定谔方程的有效势从泡利减少TBDE。我们发现，相对论薛定谔方程实际上导致良好的波函数的解决方案时，考虑到系统的全势和耦合。最不寻常的情况是S=1和L={（J-1），（J+1）}的耦合三重态系统。如果不包含张量耦合，有效S态势将变得吸引奇异。我们展示了如何包括张量耦合是必不可少的，以便波函数在短距离内表现良好。例如，与通常的S态波函数不同，S态波函数变得简单地与D态波函数成比例，并且在原点处急剧下降到零。此外，这种行为在QED和QCD中是相似的，与假设的QCD矢势的渐近自由行为无关。轻、重夸克介子态可以用一个简化的线性加库仑型QCD势来描述。我们利用这种势明确地展示了大的π-ρ分裂和有效的手征对称性破缺的起源。本文所发展的TBDE形式可用于研究夸克-胶子等离子体环境中的夸克偶素。
英文摘要：
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation lead in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.
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