# A new vacuum for loop quantum gravity

@article{Dittrich2015ANV, title={A new vacuum for loop quantum gravity}, author={Bianca Dittrich and Marc Geiller}, journal={Classical and Quantum Gravity}, year={2015}, volume={32} }

We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy–flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013…

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## References

SHOWING 1-10 OF 110 REFERENCES

Flux formulation of loop quantum gravity: classical framework

- Physics
- 2014

We recently introduced a new representation for loop quantum gravity (LQG), which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper…

Three-dimensional loop quantum gravity: physical scalar product and spin-foam models

- Physics
- 2005

In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection…

Loop Quantum Gravity

- PhysicsLiving reviews in relativity
- 2008

An overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is given, and a guide to the relevant literature is given.

Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint

- Physics
- 2012

It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a…

On loop quantum gravity kinematics with a non-degenerate spatial background

- Mathematics
- 2010

In a remarkable paper (Koslowski T A 2007 arXiv:0709.3465[gr-qc]), Koslowski introduced kinematical representations for loop quantum gravity in which a non-degenerate spatial background metric is…

On the space of generalized fluxes for loop quantum gravity

- Mathematics, Physics
- 2012

We show that the space of generalized fluxes—momentum space—for loop quantum gravity cannot be constructed by Fourier transforming the projective limit construction of the space of generalized…

Loop quantum gravity vacuum with nondegenerate geometry

- Physics
- 2012

In loop quantum gravity, states of the gravitational field turn out to be excita- tions over a vacuum state that is sharply peaked on a degenerate spatial geometry. While this vacuum is singled out…

Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity

- Physics
- 2011

In this work we investigate the canonical quantization of 2 + 1 gravity with cosmological constant Λ > 0 in the canonical framework of loop quantum gravity. The unconstrained phase space of gravity…

Loop quantum cosmology: a status report

- 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…