标题： 费米场的基本Fierz恒等式 显示英文标题

标题： Essential Fierz identities for a fermionic field

摘要： 对于单个费米子场，给出了Fierz恒等式（建立双线性场可观测量之间关系的恒等式）的一种解释。它们与与旋量场相关的自旋2-形式$S$的代数类（正则或奇异）密切相关。如果$S \neq 0$，Fierz恒等式来自于相对于惯性实验室的自旋2-形式$S$的特征向量方程的3+1分解，这使得这种解释适用于费米子粒子物理模型。当$S= 0$时，Fierz恒等式简化为与旋量场相关的电流密度的三个约束条件，即它们相互正交、模长相等，矢量电流是类时的，轴矢电流是类空的。 显示英文摘要

摘要： For a single fermionic field, an interpretation of the Fierz identities (which establish relations between the bilinear field observables) is given. They appear closely related to the algebraic class (regular or singular) of the spin 2-form $S$ associated to the spinor field. If $S \neq 0$, the Fierz identities follow from the 3+1 decomposition of the eigenvector equations for $S$ with respect to an inertial laboratory, which makes this interpretation suitable for fermionic particle physics models. When $S= 0$, the Fierz identities reduce to three constraints on the current densities associated with the spinor field, saying that they are orthogonal, equimodular, the vector current being timelike and the axial one being spacelike.