论文标题
Fermionic领域的必要Fierz身份
Essential Fierz identities for a fermionic field
论文作者
论文摘要
对于单个费米子领域，给出了对Fierz身份的解释（在双线性场观测到之间建立了关系）。它们似乎与旋转2形式的代数类（常规或单数）密切相关。如果$ s \ neq 0 $，则fierz身份来自$ s $的3+1特征向量方程相对于惯性实验室的分解，这使得这种解释适用于费米子粒子物理模型。当$ s = 0 $时，FIEZ身份在与Spinor场相关的当前密度上降低了三个约束，称它们是正交的，等的，矢量电流是时间的，并且轴向是间距。
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.
