# Quantum reduction to Bianchi I models in loop quantum gravity

@article{Bodendorfer2014QuantumRT,
title={Quantum reduction to Bianchi I models in loop quantum gravity},
author={Norbert Bodendorfer},
journal={Physical Review D},
year={2014},
volume={91},
pages={081502}
}
We propose a quantum symmetry reduction of loop quantum gravity to Bianchi I spacetimes. To this end, we choose the diagonal metric gauge for the spatial diffeomorphism constraint at the classical level, leading to an $\mathbb{R}_{\text{Bohr}}$ gauge theory, and quantise the resulting theory via loop quantum gravity methods. Constraints which lead classically to a suitable reduction are imposed at the quantum level. The dynamics of the resulting model turn out to be very simple and manifestly…
35 Citations
• Physics
• 2017
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in
• Physics
• 2020
We propose a new derivation from the full Loop Quantum Gravity (LQG) to the Loop Quantum Cosmology (LQC) improved $\bar{\mu}$-scheme effective dynamics, based on the reduced phase space formulation
Loop quantum cosmology in (b, v) variables, which is governed by a unit step size difference equation, is embedded into a full theory context based on similar variables. A full theory context here
• Physics
• 2018
We introduce a new regularization scheme for Quantum Cosmology in Loop Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG). It is obtained considering density matrices for
Canonical loop quantum gravity (LQG) is a canonical quantization of general relativity in its Hamiltonian formulation, which has successfully completed the construction of a kinematical Hilbert space
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions.
• Physics
Physical Review D
• 2019
The effective quantum dynamics of Bianchi I spacetime is addressed within the statistical regularization scheme in quantum reduced loop gravity. The case of a minimally coupled massless scalar field
• Physics
• 2016
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby
• 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
• Physics
• 2016
We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions. Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and the following expected results are

## References

SHOWING 1-10 OF 31 REFERENCES

In this paper we address the meaning of states in loop quantum cosmology (LQC), in the context of loop quantum gravity. First, we introduce a rigorous formulation of an embedding proposed by Bojowald
• Mathematics, Physics
• 2010
The relation between standard loop quantum cosmology (LQC) and full loop quantum gravity (LQG) fails already at the first nontrivial step: the configuration space of LQC cannot be embedded into the
• 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
• Physics
• 2011
Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum
An anomaly-free operator corresponding to the Wheeler - DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is
• Physics
• 2007
A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to
• Physics
• 2009
The “improved dynamics” of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and nonzero spatial curvature, certain technical
• Physics
• 2010
We compute the transition amplitude between coherent quantum states of geometry peaked on homogeneous-isotropic metrics. We work in the context of pure gravity without matter, we use the holomorphic
• Physics
• 1999
Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism-invariant theory of connections on this fibre bundle are defined. These symmetric