约束Lagrange系统理论和对称性及对不同物理系统的应用

约束Lagrange系统理论、对称性和具有约束的场论在现代物理学中居重要地位，本项目重要之点是研究约束Lagrange系统理论和对称性及对不同物理系统的应用等，研究具有约束的Lagrange系统包括场论系统的一些非常重要科学前沿的问题，同时深入地研究具有约束的Lagrange系统包括场论系统的local与nonlocal 正则symmetries、量子物理性质以及对应的守恒定 律，并深入研究广义正则Ward Identity、Anomaly和对不同相互作用系统和场等的应用，研究辛Lagrange的一般F-J（Faddeev-Jackiw）的量子理论及对不同场理论的F-J的一般量子场理论和应用等。

The theory of constraint Lagrange systems, symmetries and the field theories with realistic constraints occupy an important place in modern physics. The highlights of this project are as follows: we first investigate the theory of constraint Lagrange systems, symmetries and their applications to different physical systems, and then we study some very important scientific forefront problems of the Lagrange systems with realistic constraints including field theory systems. Meanwhile, we deeply investigate the local and nonlocal canonical symmetries, quantum physics properties and the corresponding conserved laws of the Lagrange systems with realistic constraints including field theory systems. We also make deep studies of the general canonical Ward Identity, anomaly and the applications to different interaction systems and field theories. At last, we investigate the general F-J（Faddeev-Jackiw）quantum theory of symplectic Lagrange and its applications to F-J general quantum field theory for different field theories and so on.