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http://arxiv.org/abs/gr-qc/0504147

this has been promised for a couple of years now.

here at PF we studied the papers leading up to it

there was one paper we discussed here by Lewandowski and Okolow (LO)

and several by Sahlmann and Thiemann (ST) or by Hanno Sahlmann solo.

The four of them have gotten together to prove the most general form of the LOST uniqueness theorem.

Jerzy Lewandowski, Andrzej Okolow, Hanno Sahlmann, Thomas Thiemann

38 pages, one figure

AEI-2005-093, CGPG-04/5-3

"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 cyclic representation invariant under spatial diffeomorphisms.

While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory."

this has been promised for a couple of years now.

here at PF we studied the papers leading up to it

there was one paper we discussed here by Lewandowski and Okolow (LO)

and several by Sahlmann and Thiemann (ST) or by Hanno Sahlmann solo.

The four of them have gotten together to prove the most general form of the LOST uniqueness theorem.

**Uniqueness of diffeomorphism invariant states on holonomy-flux algebras**Jerzy Lewandowski, Andrzej Okolow, Hanno Sahlmann, Thomas Thiemann

38 pages, one figure

AEI-2005-093, CGPG-04/5-3

"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 cyclic representation invariant under spatial diffeomorphisms.

While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory."

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