• DOI:10.1088/0264-9381/15/6/005
• Corpus ID: 9078812

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 which is suggested to us given the asymptotically flat structure available. The theorem demonstrates that several of the speculations regarding the stability of the theory, spelled out recently by Smolin, are false once a quantum version of the pre-assumptions underlying the classical positivity of the energy theorem is imposed in the quantum theory as well. The quantum symmetry algebra corresponding to the generators of the little group faithfully represents the classical algebra.