Nonperturbative solution of two-body Dirac equations for quantum electrodynamics and related field theories.
Nonperturbative solution of two-body Dirac equations for quantum electrodynamics and related field theories.
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DOI：
10.1103/physrevd.46.5117
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发表时间：
1992-12
期刊：
影响因子：
--
通讯作者：
Crater;Becker;Wong;Van Alstine P
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文献类型：
--
作者：
Crater;Becker;Wong;Van Alstine P
在介子谱的夸克模型计算中，由狄拉克相对论约束力学支配的全协变二体Dirac方程很好地拟合了整个介子质量谱(不包括味混合)，其组成世界标量势和矢量势仅依赖于一个或两个参数。在这篇文章中，我们通过数值求解量子电动力学(QED)和相关的场论来研究这些方程的性质，从而使它们能够很好地工作。约束形式产生了由16分量波函数上的两个耦合狄拉克方程定义的相对论量子力学，该波函数包含初始未确定的洛伦兹协变分量势。精确的Pauli约化导致了由有效相互作用-准势决定的约化八分量波函数的二阶相对论性薛定谔方程。我们首先通过将类薛定谔方程的形式与Bethe-Salpeter方程的形式进行比较，从微扰到最低阶确定了该方程的相对论准势。将这种微扰信息插入到二体狄拉克方程的最小相互作用结构中，然后完全决定了它们的相互作用结构。
In quark-model calculations of the meson spectrum, fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum (excluding flavor mixing) with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a 16-component wave function which contain Lorentz-covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second-order relativistic Schroedinger-like equation for a reduced eight-component wave function determined by an effective interaction---the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures.