This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4D. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularisations. Among various well known results we stress in particular the regularisation independence in perturbative approaches, while not all the regularisations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.

中文翻译：

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Dirac，Majorana，Weyl 4D

本文是对Dirac，Weyl和Majorana旋转器在4D中的一些基本属性的综述。我们特别关注一方面无质量的狄拉克（Dirac）和马约拉纳（Majorana）费米子，另一方面是Weyl费米子之间的差异。当与（矢量和轴向）规范场耦合时，我们将详细回顾其有效动作的定义，并使用具有不同规则性的费曼图方法重新审视相应的异常。在各种众所周知的结果中，我们特别强调扰动方法中的正则化独立性，而并非所有正则化都适合非扰动方法。对于异常，我们特别强调了一个也许不是那么广为人知的特征：手性和痕量异常之间的严格关系。