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arXiv · 1205.6166

On the space of generalized fluxes for loop quantum gravity

Bianca Dittrich·Carlos Guedes·Daniele Oriti
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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.

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Bianca Dittrich, Carlos Guedes, Daniele Oriti. 2013-02-11. On the space of generalized fluxes for loop quantum gravity. https://doi.org/10.1088/0264-9381%2F30%2F5%2F055008

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