标题： 关于马约拉纳方程——其复数两分量和实数四分量本征函数之间的关系 显示英文标题

标题： On the Majorana equation - Relations between its complex two-component and real four-component eigenfunctions

摘要： 我们首先不借助狄拉克方程，通过直接线性化具有质量项的相对论色散关系，推导出两分量马约拉纳方程。在此过程中，我们仅使用复共轭算符和泡利自旋矩阵，对应于洛伦兹群的不可约表示。然后，我们通过利用所谓的手征共轭算符，以简洁的方式推导出马约拉纳方程的复两分量本征函数及其相关的量子场，该算符涉及自旋翻转算符。随后，推导出实马约拉纳方程的四分量旋量解，并广泛揭示和讨论它们与复两分量马约拉纳方程旋量之间的内在关系。 显示英文摘要

摘要： We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex conjugation operator and the Pauli spin matrices, corresponding to the irreducible representation of the Lorentz group. Then we derive the complex two-component eigenfunctions of the Majorana equation and the related quantum fields in a concise way, by exploiting the so called chirality conjugation operator that involves the spin-flip operator. Subsequently, the four-component spinor solutions of the real Majorana equation are derived, and their intrinsic relations with the spinors of the complex two-component version of the Majorana equation are revealed and discussed extensively.