Uniqueness of diffeomorphism invariant states on holonomy-flux algebras

Journal article
(Original article)

Publication Details

Author(s): Lewandowski J, Okolow A, Sahlmann H, Thiemann T
Journal: Communications in Mathematical Physics
Publisher: Springer Verlag (Germany)
Publication year: 2006
Volume: 267
Journal issue: 3
Pages range: 703-733
ISSN: 0010-3616


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.

FAU Authors / FAU Editors

Lewandowski, Jerzy
Lehrstuhl für Theoretische Physik
Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik

How to cite

Lewandowski, J., Okolow, A., Sahlmann, H., & Thiemann, T. (2006). Uniqueness of diffeomorphism invariant states on holonomy-flux algebras. Communications in Mathematical Physics, 267(3), 703-733. https://dx.doi.org/10.1007/s00220-006-0100-7

Lewandowski, Jerzy, et al. "Uniqueness of diffeomorphism invariant states on holonomy-flux algebras." Communications in Mathematical Physics 267.3 (2006): 703-733.


Last updated on 2018-31-10 at 13:50