Holst和Plebanski引力的正则路径积分测度。I.简化相空间推导
Canonical path integral measures for Holst and Plebanski gravity. I. Reduced Phase Space Derivation
摘要：
在定义路径积分的量子理论的一个重要方面是确定正确的措施。对于相互作用的理论和有约束的理论，这是不平凡的，通常不是通常使用的启发式“勒贝格测度”。在文献中有许多关于重力的测量的确定，但没有关于帕拉蒂尼或霍尔斯特重力公式的确定。此外，通常不讨论不同重力公式的不同结果测量之间的关系。本文利用约化相位技术导出了Palatini和Holst引力公式的路径积分测度，它不同于Lebesgue测度，直到局部测度因子依赖于时空体元和空间体元。从这个路径积分的霍尔斯特制定的GR，我们也可以给一个新的推导Plebanski路径积分，并发现一个差异的结果，由于Buffenoir，Henneaux，Noui和罗氏（BHNR）的起源，我们解决。本文是第一个系列，旨在更好地理解规范LQG和自旋泡沫方法之间的关系。
英文摘要：
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure" usually used. There have been many determinations of a measure for gravity in the literature, but none for the Palatini or Holst formulations of gravity. Furthermore, the relations between different resulting measures for different formulations of gravity are usually not discussed. In this paper we use the reduced phase technique in order to derive the path-integral measure for the Palatini and Holst formulation of gravity, which is different from the Lebesgue measure up to local measure factors which depend on the spacetime volume element and spatial volume element. From this path integral for the Holst formulation of GR we can also give a new derivation of the Plebanski path integral and discover a discrepancy with the result due to Buffenoir, Henneaux, Noui and Roche (BHNR) whose origin we resolve. This paper is the first in a series that aims at better understanding the relation between canonical LQG and the spin foam approach.
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