# 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

### New Hamiltonians for loop quantum cosmology with arbitrary spin representations

- 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…

### Improved μ¯ -scheme effective dynamics of full loop quantum gravity

- 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…

### An embedding of loop quantum cosmology in ( b , v ) variables into a full theory context

- Physics
- 2016

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…

### Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

- 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…

### New dynamics for canonical loop quantum gravity

- Mathematics
- 2016

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…

### Higher dimensional loop quantum cosmology

- Physics
- 2015

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.…

### Bianchi I effective dynamics in quantum reduced loop gravity

- PhysicsPhysical 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…

### Diffeomorphism invariant cosmological symmetry in full quantum gravity

- 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…

### Effective dynamics from coherent state path integral of full loop quantum gravity

- PhysicsPhysical 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…

### (2+1)-dimensional loop quantum cosmology of Bianchi I models

- 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…

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