On the relation between operator constraint, master constraint, reduced phase space and path integral quantization

@article{Han2010OnTR,
  title={On the relation between operator constraint, master constraint, reduced phase space and path integral quantization},
  author={Muxin Han and Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={2010},
  volume={27},
  pages={225019}
}
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 paper 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 quantization and, more specifically, with the master constraint quantization… 
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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
Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from
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