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 ≠ 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:

Physica Scripta
 Pub Date:
 August 2023
 DOI:
 10.1088/14024896/ace1b3
 arXiv:
 arXiv:2206.00639
 Bibcode:
 2023PhyS...98h5302D
 Keywords:

 fermionic fields;
 Fierz identities;
 spin 2form density;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 17 pages