The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

中文翻译：

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空间平坦 FLRW 时空中自由狄拉克场的时间演化

考虑空间平坦 FLRW 时空上的相对论量子力学框架，以在这些流形的不同局部图表中推导狄拉克方程的解析解。通勤守恒算子系统用于将基本解确定为公共特征旋量，从而为与这些算子的特征值相关的积分常数赋予物理意义。由于这些系统通常在 FLRW 时空上是不完整的，因此必须通过将真空设置为传统的绝热真空或我们最近提出的静止框架真空来固定积分常数。