标题： 狄拉克类方法在经典约束理论一致离散化中的应用 显示英文标题

标题： Dirac-like approach for consistent discretizations of classical constrained theories

摘要： 我们分析了用离散时间形式化的经典约束力学系统的规范处理。我们证明，在非常一般的情况下，可以引入非奇异的规范变换，这些变换保持约束曲面和泊松括号或狄拉克括号结构。保持约束的条件比连续情况下更为严格，因此一些连续约束在离散化后变为第二类约束，需要通过固定相关的拉格朗日乘子来解决。离散理论的规范不变性编码在演化方程生成函数中的一组任意函数中。所得方案足够通用，可以容纳格点场论的处理。本文试图澄清并为已经用于处理包括杨-米尔斯理论、BF理论和格点广义相对论在内的各种系统的离散化技术奠定更坚实的基础。 显示英文摘要

摘要： We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the Poisson or Dirac bracket structure. The conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated Lagrange multipliers. The gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations. The resulting scheme is general enough to accommodate the treatment of field theories on the lattice. This paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems, including Yang--Mills theories, BF-theory and general relativity on the lattice.