Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory

@article{Giesel2006AlgebraicQG,
  title={Algebraic quantum gravity (AQG): III. Semiclassical perturbation theory},
  author={Kristina Giesel and Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={2006},
  volume={24},
  pages={2565-2588}
}
In the two previous papers of this series we defined a new combinatorical approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics in the semiclassical limit, provided one incorrectly substitutes the non – Abelean group SU(2) by the Abelean group U(1) 3 in the calculations. The mere reason why that substitution was performed at all is that in the non – Abelean case the volume operator, pivotal for the definition of the… 
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References

SHOWING 1-10 OF 47 REFERENCES
Algebraic quantum gravity (AQG): II. Semiclassical analysis
In the previous paper (Giesel and Thiemann 2006 Conceptual setup Preprint gr-qc/0607099) a new combinatorial and thus purely algebraical approach to quantum gravity, called algebraic quantum gravity
Simplification of the spectral analysis of the volume operator in loop quantum gravity
The volume operator plays a crucial role in the definition of the quantum dynamics of loop quantum gravity (LQG). Efficient calculations for dynamical problems of LQG can therefore be performed only
Algebraic Quantum Gravity (AQG). I. Conceptual Setup
We introduce a new top down approach to canonical quantum gravity, called algebraic quantum gravity (AQG). The quantum kinematics of AQG is determined by an abstract *-algebra generated by a
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
Lectures on Loop Quantum Gravity
AbstractQuantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured overthe past fifteen years to a mathematically rigorous candidate quantum field theory of the gravita-tional
Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity
The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and
Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
In the canonical approach to Lorentzian quantum general relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through
Quantum spin dynamics: VIII. The master constraint
Recently the master constraint programme (MCP) for loop quantum gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single master constraint. The MCP is
Quantum spin dynamics (QSD): VI. Quantum Poincaré algebra and a quantum positivity of energy theorem for canonical quantum gravity
We quantize the generators of the little subgroup of the asymptotic Poincare group of Lorentzian four-dimensional canonical quantum gravity in the continuum. In particular, the resulting ADM energy
QSD V : Quantum Gravity as the Natural Regulator 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
...
1
2
3
4
5
...