arXiv 2005.090612020-05quant-phhep-th

狄拉克振子的不同电磁物理表示与其空间维数的一致性

Different electromagnetic physical representations of the Dirac's oscillator according with its spatial dimension

Juan Sebastián Montañez Moyano, Carlos José Quimbay Herrera

备注：: 15 pages

摘要：

狄拉克振子是相对论量子力学和物理数学中研究最多的系统之一。特别是，我们表明，该系统具有独特的属性，它从来没有见过在其他已知的系统：根据其空间维度，DO代表物理系统具有非常不同的电磁性质。到目前为止，文献中已经用协变方法证明了狄拉克振子势的规范不变性。在（3+1）维中，DO代表一个相对论性的电中性费米子，它具有磁偶极子动量，在一个依赖于径向距离的电场作用下，进入一个球对称的电介质中.在这项工作中，并使用相同的方法，我们表明，（2+1）维DO表示1/2自旋相对论费米子的影响下，一个均匀和垂直的外部磁场，而在（1+1）维DO再现相对论和带电费米子与线性电场相互作用。此外，我们证明了DO不具有手征不变性，独立于它的维数，由于相互作用势明确地打破了手征对称性$U(1)_R \times U(1)_L$，但它保留了全球规范对称性$U(1)$。

英文摘要：

Dirac's oscillator (DO) is one of the most studied systems in the Relativistic Quantum Mechanics and in the physical-mathematics. In particular, we show that this system has an unique property which it has not ever seen in other known systems: According to its spatial dimensionality, DO represent physical systems with very different electromagnetic nature. So far in the literature, it has been proved using the covariant method the gauge invariance of the Dirac's oscillator potential. It has also shown that in (3+1)dimensions the DO represents a relativistic and electrically neutral fermion with magnetic dipole momentum, into a dielectric medium with spherical symmetry and under the effect of an electric field which depends of the radial distance. In this work,and using the same methodology, we show that (2+1) dimensional DO represents a 1/2-spin relativistic fermion under the effect of a uniform and perpendicular external magnetic field; whereas in (1+1) dimensions DO reproduces a relativistic and electrically charged fermion interacting with a linear electric field. Additionally, we prove that DO does not have chiral invariance, independent of its dimensionality, due to the interaction potential which breaks explicitly the chiral symmetry $U(1)_R \times U(1)_L$ but it preserves the global gauge symmetry $U(1)$.

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