Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras

  title={Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras},
  author={Jerzy Lewandowski and Andrzej Okoł{\'o}w and H. Sahlmann and Thomas Thiemann},
  journal={Communications in Mathematical Physics},
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one… 
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