# 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…

## 32 Citations

Canonical path integral measures for Holst and Plebanski gravity: I. Reduced phase space derivation

- Mathematics
- 2009

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

- Physics
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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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Canonical quantization of constrained systems with first-class constraints via Dirac’s operator constraint method proceeds by the theory of Rigged Hilbert spaces, sometimes also called refined…

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A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce…

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Spin-foam models are supposed to be discretized path integrals for quantum gravity constructed from the Plebanski–Holst action. The reason for there being several models currently under consideration…

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The quantization of the gravitational interaction is a major open challenge in theoretical physics. This review presents the status of the spin foam approach to the problem. Spin foam models are…

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Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the…

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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

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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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