Geometric Structures and Gauge Symmetries for Various Fermionic Fields from a Faddeev–Jackiw–Dirac Argument

This paper focuses on the identification of presymplectic/symplectic structures, as well as gauge symmetries, for various fermionic fields in four spacetime dimensions, using a combined Faddeev–Jackiw–Dirac approach. The intrinsic first-order dynamics of fermionic fields allow a straightforward Faddeev–Jackiw analysis, which avoids unnecessary primary second-class constraints, introduces no artificial hierarchies, and, in general, constitutes a foolproof strategy when combined with the Dirac method. The Majorana spinors and Majorana spinor-vectors, with dynamics of various orders, as fundamental constituents of all SUSY and SUGRA paradigms, are here taken into consideration. Their Faddeev–Jackiw–Dirac analysis exhibits several symplectic/presymplectic structures, which represent the main novelty, together with the reconfirmation of their gauge symmetries.