Quantum geometry with intrinsic local causality

@article{Markopoulou1997QuantumGW,
  title={Quantum geometry with intrinsic local causality},
  author={Fotini Markopoulou and Lee Smolin},
  journal={Physical Review D},
  year={1997},
  volume={58},
  pages={084032}
}
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 labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group ${G}_{q}$ over all compact (finite genus) oriented 2-surfaces. The dynamics is background independent and locally causal. The dynamics constructs… 
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References

SHOWING 1-10 OF 89 REFERENCES

The geometry of quantum spin networks

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…

Spin networks and quantum gravity.

  • RovelliSmolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.

The physical hamiltonian in non-perturbative quantum gravity

A quantum Hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop…

Loop space representation of quantum general relativity

Linking topological quantum field theory and nonperturbative quantum gravity

Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the…

A length operator for canonical quantum gravity

We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is…

Quantum deformation of quantum gravity

'Sum over surfaces' form of loop quantum gravity

We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We…

The physical Hamiltonian in nonperturbative quantum gravity.

A quantum Hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop…

Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague…
...