Andrzej Okołów and Jerzy Lewandowski 2005 Class. Quantum Grav. 22 657 doi:10.1088/0264-9381/22/4/002
Automorphism covariant representations of the holonomy-flux 
-algebra
Andrzej Okołów1 and Jerzy Lewandowski1,2
Show affiliationsWe continue the analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of loop quantum gravity. We consider an arbitrary principal bundle of a compact connected structure group and, following Sahlmann's ideas (Sahlmann 2002 Preprint gr-qc/0207111), define a holonomy-flux -algebra whose elements correspond to the elementary variables. There exists a natural action of automorphisms of the bundle on the algebra; this action generalizes the action of analytic diffeomorphisms and gauge transformations on the algebra considered in earlier works. We define the automorphism covariance of a -representation of the algebra on a Hilbert space and prove that the only Hilbert space admitting such a representation is a direct sum of the spaces L2, given by a unique measure on the space of generalized connections. This result is a generalization of our previous work (Okołów and Lewandowski 2003 Class. Quantum Grav. 20 3543–67 (Preprint gr-qc/0302059)) where we assumed that the principal bundle is trivial and its base manifold is 
.
- PACS
-
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
02.10.-v Logic, set theory, and algebra
- MSC
- Subjects
- Dates
-
Issue 4 (21 February 2005)
Received 22 October 2004, in final form 15 December 2004
Published 24 January 2005
-
Automorphism covariant representations of the holonomy-flux -algebra
Andrzej Okołów and Jerzy Lewandowski 2005 Class. Quantum Grav. 22 657
-
Formation and reactivity of CrII carbonyls hosted in polar and non polar supports
D Gianolio et al 2009 J. Phys.: Conf. Ser. 190 012140
-
The 2-link periodic orbits which maximize or minimize the length of a p-dimensional Birkhoff billiard are hyperbolic
Marie-Claude Arnaud 2002 Nonlinearity 15 1755
-
Multi-operator brackets acting thrice
Thomas Curtright et al 2009 J. Phys. A: Math. Theor. 42 462001
-
On the origin and nature of finite-amplitude instabilities in physical systems
R Krechetnikov and J E Marsden 2009 J. Phys. A: Math. Theor. 42 412004
-
The ground state of chargeless fermions with finite magnetic moment
S D Mahanti and Sudhanshu S Jha 2006 J. Phys. A: Math. Gen. 39 1239
-
Uncertainty evaluation associated with fitting geometric surfaces to coordinate data
Alistair B Forbes 2006 Metrologia 43 S282
-
Absorption profile at surfaces
P M Echenique and J B Pendry 1975 J. Phys. C: Solid State Phys. 8 2936
-
Submillimeter Observations of Titan: Global Measures of Stratospheric Temperature, CO, HCN, HC3N, and the Isotopic Ratios 12C/13C and 14N/15N
Mark A. Gurwell 2004 ApJ 616 L7
-
Twin Markovian field correlation on four-level attosecond polarization beats
Yanpeng Zhang et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 1751
Related review articles
What's this?- Loop quantum cosmology: a status report
- Tunnelling methods and Hawking's radiation: achievements and prospects
- Quantitative approaches to information recovery from black holes
