Essential Fierz identities for a fermionic field
Abstract
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 2form $S$ 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.00639
 Bibcode:
 2022arXiv220600639D
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 17 pages