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arXiv 0907.0051hep-ph
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Dirac方程的对称性及其唯象性

Symmetry of Dirac Equation and Corresponding Phenomenology

Hong-Wei Ke, Zuo Li, Jing-Ling Chen, Yi-Bing Ding, Xue-Qian Li

摘要:

有人认为,具有库仑势或谐振子势的薛定谔方程中的高度对称性可能保留在相应的相对论狄拉克方程中。如果该原理正确,狄拉克方程中的势应具有${(1+β)\over 2}V(r)$的形式,其中$V(r)$对氢原子为${-e^2\over r}$,对谐振子为$κr^2$.然而,在氢原子的情况下,通过这种组合,自旋-轨道耦合项将不存在,这与氢原子的观测谱不一致,因此SO(4)的对称性必然退化为SU(2)。诱导势的控制机制QED和QCD是类矢量理论,因此在首阶只存在矢量势。然而,高阶效应可能导致标量分数。本文证明了QED的对称性恢复是很小的,并对对称性破缺进行了讨论。最后,我们简要地讨论了QCD的情况,指出QCD的情况要复杂得多,也有趣得多。

英文摘要:

It has been suggested that the high symmetries in the Schrödinger equation with the Coulomb or harmonic oscillator potentials may remain in the corresponding relativistic Dirac equation. If the principle is correct, in the Dirac equation the potential should have a form as ${(1+β)\over 2}V(r)$ where $V(r)$ is ${-e^2\over r}$ for hydrogen atom and $κr^2$ for harmonic oscillator. However, in the case of hydrogen atom, by this combination the spin-orbit coupling term would not exist and it is inconsistent with the observational spectra of hydrogen atom, so that the symmetry of SO(4) must reduce into SU(2). The governing mechanisms QED and QCD which induce potential are vector-like theories, so at the leading order only vector potential exists. However, the higher order effects may cause a scalar fraction. In this work, we show that for QED, the symmetry restoration is very small and some discussions on the symmetry breaking are made. At the end, we briefly discuss the QCD case and indicate that the situation for QCD is much more complicated and interesting.

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。

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