Quantum spin dynamics (QSD): VI. Quantum Poincaré algebra and a quantum positivity of energy theorem for canonical quantum gravity

@article{Thiemann1997QuantumSD,
  title={Quantum spin dynamics (QSD): VI. Quantum Poincar{\'e} algebra and a quantum positivity of energy theorem for canonical quantum gravity},
  author={Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={1997},
  volume={15},
  pages={1463-1485}
}
  • T. Thiemann
  • Published 10 May 1997
  • Mathematics, Physics
  • Classical and 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 operator is densely defined on an appropriate Hilbert space, symmetric and essentially self-adjoint. Moreover, we prove a quantum analogue of the classical positivity of the energy theorem due to Schoen and Yau. The proof uses a certain technical restriction on the space of states at spatial infinity… 
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This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed
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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
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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
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We determine the complete and rigorous kernel of the Wheeler - DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum. We do
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