# Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product

@article{Han2009CanonicalPM,
title={Canonical Path-Integral Measures for Holst and Plebanski Gravity. II. Gauge Invariance and Physical Inner Product},
author={Muxin Han},
journal={Classical and Quantum Gravity},
year={2009},
volume={27},
pages={245015}
}
• Muxin Han
• Published 17 November 2009
• Physics
• Classical and Quantum Gravity
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 canonical framework and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory. This paper is divided into two parts, the first part is…
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
Purely geometric path integral for spin foams
• Physics
• 2014
Spin-foams are a proposal for defining the dynamics of loop quantum gravity via path integral. In order for a path integral to be at least formally equivalent to the corresponding canonical
On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
• Physics
• 2010
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
The Holst Spin Foam Model via Cubulations
• Physics
• 2012
Spin foam models are an attempt for a covariant, or path integral formulation of canonical loop quantum gravity. The construction of such models usually rely on the Plebanski formulation of general
Spin Foams and Canonical Quantization
• Physics
• 2012
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the
On the relation of canonical and covariant formulations of Loop Quantum Gravity
Loop Quantum Gravity (LQG) is a background independent approach towards a quantum theory of gravity that splits into a canonical and a covariant branch the latter of which is also often called spin
A path integral for the master constraint of loop quantum gravity
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. The physical inner product is expressed by using the group averaging technique for
M ay 2 01 2 The new spin foam models and quantum gravity
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
Effective dynamics from coherent state path integral of full loop quantum gravity
• Physics
Physical Review D
• 2020
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
Gravitational path integral from the T 2 deformation
• Mathematics
• 2020
We study a $T^2$ deformation of large $N$ conformal field theories, a higher dimensional generalization of the $T\bar T$ deformation. The deformed partition function satisfies a flow equation of the

## References

SHOWING 1-10 OF 49 REFERENCES
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
On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
• Physics
• 2010
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
Generally covariant theories: the Noether obstruction for realizing certain space–time diffeomorphisms in phase space
Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms being
Reduced phase space quantization and Dirac observables
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint
Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order
• Physics
• 2007
In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless
Quantization of Gauge Systems
• Physics
• 1992
This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical
Partial and complete observables for Hamiltonian constrained systems
We will pick up the concepts of partial and complete observables introduced by Rovelli in Conceptional Problems in Quantum Gravity, Birkhäuser, Boston (1991); Class Quant Grav, 8:1895 (1991); Phys
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
• Physics
• 2010
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the
Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
• Physics
• 1997
We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators
A path integral for the master constraint of loop quantum gravity
In the present paper, we start from the canonical theory of loop quantum gravity and the master constraint program. The physical inner product is expressed by using the group averaging technique for