A Darboux-Theorem-Based Derivation of Geometric Structures in Various Non-Abelian Gauge Theories
arXiv:2607.27417
The paper uses the Faddeev–Jackiw approach to systematically derive the phase‑space, symplectic structure, constraints, Hamiltonian, and gauge transformations for several non‑Abelian gauge theories such as Freedman–Townsend, Yang–Mills, and BF models.
Abstract
This paper illustrates the straightforward application of the Faddeev--Jackiw approach to several non-Abelian gauge theories, namely, the Freedman--Townsend, Yang--Mills, and non-Abelian BF models, as well as a nonlinear theory of BF type. For each theory, the procedure determines the phase space and its symplectic structure, the coisotropic constraint submanifold, the Hamiltonian, and the reducibility properties of the constraints. By combining these results with the Dirac conjecture, one reconstructs through direct computation the corresponding Lagrangian gauge transformations and their reducibility structure. The analysis provides a unified and efficient derivation of the principal Hamiltonian and Lagrangian gauge structures of these non-Abelian theories.
16 pages, no figures