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On the space of generalized fluxes for loop quantum gravity

MPS-Authors
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Dittrich,  Bianca
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Guedes,  Carlos
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1205.6166
(Preprint), 396KB

CQG_30_5_055008.pdf
(Any fulltext), 558KB

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Citation

Dittrich, B., Guedes, C., & Oriti, D. (2013). On the space of generalized fluxes for loop quantum gravity. Classical and quantum gravity, 3(5): 055008. doi:10.1088/0264-9381/30/5/055008.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-E979-7
Abstract
We show that the space of generalized fluxes - momentum space - for loop quantum gravity cannot be constructed by Fourier transforming the projective limit construction of the space of generalized connections - position space - due to the non-abelianess of the gauge group SU(2). From the abelianization of SU(2), U(1)^3, we learn that the space of generalized fluxes turns out to be an inductive limit, and we determine the consistency conditions the fluxes should satisfy under coarse-graining of the underlying graphs. We comment on the applications to loop quantum cosmology, in particular, how the characterization of the Bohr compactification of the real line as a projective limit opens the way for a similar analysis for LQC.