On the space of generalized fluxes for loop quantum gravity
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.
Keywords
Cite
@article{arxiv.1205.6166,
title = {On the space of generalized fluxes for loop quantum gravity},
author = {Bianca Dittrich and Carlos Guedes and Daniele Oriti},
journal= {arXiv preprint arXiv:1205.6166},
year = {2013}
}
Comments
25 pages, 2 figures; matches published version