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

@article{Thiemann1998QuantumSD,
  title={Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories},
  author={Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={1998},
  volume={15},
  pages={1281-1314}
}
  • T. Thiemann
  • Published 1 May 1998
  • Physics
  • Classical and Quantum Gravity
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 quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a… 
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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
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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
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