约束系统理论和约束场论在现代物理学中处于重要地位，本科研项目重点研究约束系统理论和对不同量子化理论与对应的场论等的应用，研究约束Hamilton场论系统和约束Lagrange场论系统中的一些重要的前沿问题，并且不但深入研究约束系统场论的定域与非定域Canonical对称性、量子性质和守恒律，而且还深入地究求其相关的广义Canonical Ward恒等式、反常、对不同基本相互作用场等的应用，研究Faddeev-Jackiw（FJ）量子化方法与其它量子化方法的关系及其应用，研究不同场的FJ量子场论及其应用等。

Constrained system theory and constrained field theory play very important roles in modern physics, this scientific program mainly investigates constrained system theory and its applications to different quantization theories and corresponding field theories and so on, and studies some important fronting problems in constrained Hamilton field system and constrained Lagrange field system. The program not only investigates local and nonlocal canonical symmetric properties, quantum properties and conservation laws, but also deeply explores and investigates generally canonical Ward identity and relative anomalies of the constrained system field theory and their applications to different fundamental interaction fields and so on. The program studies Faddeev-Jackiw（FJ）quantization method and their relations with the other quantization methods and their applications, investigates FJ quantum field theory and its applications and so on.