算子约束、主约束、约化相空间与路径积分量化的关系
On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation
摘要：
规范理论的路径积分公式必须从正则公式出发，才能得到正确的测度。一个可能的途径来获得它是从减少相空间公式开始。在这篇文章中，我们回顾了这一相当复杂的程序在充分的一般性。此外，我们证明，减少相空间路径积分制定正式同意狄拉克的运营商约束量化，更具体地说，与主约束量化的第一类约束。对于具有非平凡结构函数的第一类约束，等价只能通过传递到阿贝尔约束来建立，阿贝尔约束在相空间中总是局部可能的。一般地，正确的位形空间路径积分测度偏离拉格朗日作用量的指数。如果理论受到第二类次级约束，则修正尤其严重。在一个配套文件中，我们计算这些校正的霍尔斯特和普莱班斯基配方的GR目前的自旋泡沫模型的基础上。
英文摘要：
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
