Quantum theory of geometry: I. Area operators

@article{Ashtekar1996QuantumTO,
  title={Quantum theory of geometry: I. Area operators},
  author={Abhay Ashtekar and Jerzy Lewandowski},
  journal={Classical and Quantum Gravity},
  year={1996},
  volume={14}
}
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 operators corresponding to areas of 2-surfaces are introduced and shown to be self-adjoint on the underlying (kinematical) Hilbert space of states. It is shown that their spectra are purely discrete, indicating that the underlying quantum geometry is far from what the continuum picture might suggest. Indeed… 
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