# Spin networks and quantum gravity.

@article{Rovelli1995SpinNA, title={Spin networks and quantum gravity.}, author={Rovelli and Smolin}, journal={Physical review. D, Particles and fields}, year={1995}, volume={52 10}, pages={ 5743-5759 } }

We introduce a new basis on the state space of non-perturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representation, and are labeled by a generalization of Penrose's spin netoworks. The new basis fully reduces the spinor identities (SU(2) Mandelstam identities) and simplifies calculations in non-perturbative quantum gravity. In particular, it allows a simple expression for the exact solutions of…

## 543 Citations

Quantum Spin Dynamics (QSD)

- Physics
- 1998

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…

Quantum spin dynamics (QSD)

- Physics
- 1998

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…

Quantum gravity vacuum and invariants of embedded spin networks

- Physics
- 2003

We show that the path integral for the three-dimensional SU (2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a…

The geometry of quantum spin networks

- Physics
- 1996

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation of the observable algebra. Operators for area and volume are extended…

The geometry of quantum spin networks

- Physics
- 1996

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation of the observable algebra. Operators for area and volume are extended…

On loop states in loop-quantum gravity

- Physics
- 2006

We explicitly construct and characterize all possible independent loop states in (3 + 1)-dimensional loop-quantum gravity by regulating it on a 3D regular lattice in the Hamiltonian formalism. These…

Quantum geometry with intrinsic local causality

- Physics, Mathematics
- 1998

The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by…

Fusion basis for lattice gauge theory and loop quantum gravity

- Physics
- 2016

A bstractWe introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2 + 1) dimensions, the fusion basis. In doing so, we shift the focus from…

Observables in quantum gravity

- Physics
- 2001

We study a family of physical observable quantities in quantum gravity. We denote them W functions, or n-net functions. They represent transition amplitudes between quantum states of the geometry,…

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