Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417736 | Journal of Mathematical Analysis and Applications | 2015 | 30 Pages |
Projective structures have successfully been used for the construction of measures in the framework of loop quantum gravity. In the present paper, we establish such structures for the configuration space RâRBohr, recently introduced in the context of homogeneous isotropic loop quantum cosmology. In contrast to the traditional space RBohr, the first one is canonically embedded into the quantum configuration space of the full theory. In particular, for the embedding of states into a corresponding symmetric sector of loop quantum gravity, this is advantageous. However, in contrast to the traditional space, there is no Haar measure on RâRBohr defining a canonical kinematical L2-Hilbert space on which operators can be represented. The introduced projective structures allow to construct a family of natural measures on RâRBohr whose corresponding L2-Hilbert spaces we finally investigate.