AI 中文总结
本文将Faddeev-Jackiw方法应用于多种非阿贝尔规范理论，结合Dirac猜想推导其几何结构，实现了规范结构的统一高效推导。
AI 中文摘要
本文展示了Faddeev-Jackiw方法在多种非阿贝尔规范理论中的直接应用，包括Freedman-Townsend模型、Yang-Mills模型、非阿贝尔BF模型以及一种非线性BF型理论。对每种理论，该方法确定了相空间及其辛结构、余迷向约束子流形、哈密顿量和约束的可约性性质。结合这些结果与Dirac猜想，通过直接计算可重构出对应的拉格朗日规范变换及其可约结构。该分析为这些非阿贝尔理论的主要哈密顿和拉格朗日规范结构提供了统一且高效的推导方式。
英文摘要
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.
Comments16 pages, no figures
