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          Institute: MPI für Gravitationsphysik     Collection: Quantum Gravity and Unified Theories     Display Documents

ID: 221776.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Uniqueness of Diffeomorphism Invariant States on Holonomy - Flux Algebras
Authors:Lewandowski, Jerzy; Okolow, Andrzej; Sahlmann, Hanno; Thiemann, Thomas
Date of Publication (YYYY-MM-DD):2006
Title of Journal:Communications in Mathematical Physics
Issue / Number:3
Start Page:703
End Page:733
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
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