相对论电动力学中规范场相互作用的有效Dirac代数
The effective Dirac algebra by gauge field interaction in relativistic electrodynamics
摘要：
传统的相对论电动力学是建立在平坦的闵可夫斯基时空上的，其中所有可计算的量都是从平坦度规$η_{μν}$计算的。我们可以从狄拉克代数重新定义时空的度规。在本文中，我们研究了如何电动相互作用可以改变正常的伽玛矩阵的有效之一，并导致移动的度规微扰。从弯曲度量推断的曲率性质也进行了研究。我们还研究了自旋算符如何在有效自旋算符的相互作用下发生变化，以及电子的自旋如何轻微偏离$1/2$。然后对有效狄拉克代数进行正则量子化。最后，我们将结果应用到相对论氢的情形，并演示了这样的系统如何弯曲时空度规。
英文摘要：
Conventional relativistic electrodynamics is set on flat Minkowski spacetime, where all computable quantities are calculated from the flat metric $η_{μν}$. We can redefine the metric of spacetime from the Dirac algebra. In this paper, we study how an electrodynamic interaction can alter the normal gamma matrix to an effective one and result in a shift in the metric perturbatively. The curvature properties inferred from the curved metric are also investigated. We also study how the spin operator is changed under the interaction that contribute to an effective spin operator and how the spin of an electron will be slightly deviated from $1/2$. Then we perform canonical quantization of the effective Dirac algebra. Finally we apply our results to the relativistic hydrogen case and demonstrate how such system curves the spacetime metric.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
