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… 

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References

SHOWING 1-10 OF 31 REFERENCES

Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings

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

Symmetry reduction of loop quantum gravity

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

A quantum reduction to spherical symmetry in loop quantum gravity

Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity

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

Loop quantum cosmology: a status report

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

Quantum Spin Dynamics (QSD)

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

Polymer Quantum Mechanics and its Continuum Limit

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

Loop quantum cosmology of Bianchi type II models

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

Towards spinfoam cosmology

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

Symmetry reduction for quantized diffeomorphism-invariant theories of connections

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