Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity

@article{Thiemann1996AnomalyfreeFO,
  title={Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity},
  author={Thomas Thiemann},
  journal={Physics Letters B},
  year={1996},
  volume={380},
  pages={257-264}
}
  • T. Thiemann
  • Published 29 June 1996
  • Physics
  • Physics Letters B
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References

SHOWING 1-10 OF 54 REFERENCES
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
Constraint quantization of parametrized relativistic gauge systems in curved spacetimes.
The Dirac constraint quantization of a finite-dimensional relativistic gauge system with a quadratic super-Hamiltonian and linear supermomenta is investigated as a model for quantizing generally
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
Real alternative to quantum gravity in loop space.
  • Loll
  • Physics
    Physical review. D, Particles and fields
  • 1996
We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined on a space of real, SU(2)-valued connections, in spite of its non-polynomiality possesses a natural quantum analogue in a
Spin networks and quantum gravity.
  • Rovelli, Smolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
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 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 theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated
Transversal affine connection and quantization of constrained systems
The Dirac quantization of a finite‐dimensional relativistic system with a quadratic super‐Hamiltonian and linear supermomenta is investigated. In a previous work, the operator constraints were
Quantum linearization instabilities of de Sitter spacetime. II
It is known that all the physical states in linearized gravity are required to be invariant under the continuous isometries of the background spacetime if it is spatially compact. For example, all
...
1
2
3
4
5
...