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Journal Article

#### On the space of generalized fluxes for loop quantum gravity

##### MPS-Authors

##### Locator

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##### Fulltext (public)

1205.6166

(Preprint), 396KB

CQG_30_5_055008.pdf

(Any fulltext), 558KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.