论文标题
量规理论中的普遍规范方法的变形问题
Generalized canonical approach to deformation problem in gauge theories
论文作者
论文摘要
我们开发了一种构造变形的通用方法，该变形描述了在相位空间中具有不可还原的一流约束的任何动态系统的映射，以带有具有一流约束的另一个动态系统。结果表明，在Batalin-Fradkin-Vilkovisky（BFV）形式主义的框架中，可以有效地探索这种变形问题。这种形式主义的基本对象是BRST-BFV电荷和广义的哈密顿量，它以（Super）Poisson括号来满足扩展相空间中的定义方程式。通过（超级）规范转换具有特殊生成函数，可以明确确定变形问题的一般解决方案。证明该生成函数由单个任意函数决定，该功能仅取决于初始动力学系统的坐标。原则上，这样的功能可能是非本地的，但是变形理论可能具有局部部门。为了说明开发的方法，我们已将亚伯量规理论的非本地变形构建为非本地非亚伯利亚仪表理论，该理论的本地部门与标准的Yang-Mills理论一致。
We develop a general approach to constructing a deformation that describes the mapping of any dynamical system with irreducible first-class constraints in the phase space into another dynamical system with first-class constraints. It is shown that such a deformation problem can be efficiently explored in the framework of the Batalin-Fradkin-Vilkovisky (BFV) formalism. The basic objects of this formalism are the BRST-BFV charge and a generalized Hamiltonian that satisfy the defining equations in the extended phase space in terms of (super)Poisson brackets. General solution to the deformation problem is found in terms of a (super)canonical transformation with a special generating function which is explicitly established. It is proved that this generating function is determined by a single arbitrary function which depends only on coordinates of initial dynamical system. In principle, such a function may be non-local, but the deformed theory may have a local sector. To illustrate the developed approach, we have constructed a non-local deformation of the Abelian gauge theory into a non-local non-Abelian gauge theory whose local sector coincides with the standard Yang-Mills theory.
