Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Loop Quantization and Symmetry: Configuration Spaces   Given two sets $S_1, S_2$ and unital C*-algebras $A_1$, $A_2$ of functions
thereon, we show that a map $\sigma : S_1 \nach S_2$ can be lifted to a
continuous map $\bar\sigma : \spec A_1 \to \spec A_2$ iff $\sigma^\ast A_2 :=
\{\sigma^\ast f | f \in A_2\} \subset A_1$. Moreover, $\overline\sigma$ is
unique if existing, and injective iff $\sigma^\ast A_2$ is dense.
  Then, we apply these results to loop quantum gravity and loop quantum
cosmology. Here, the quantum configuration spaces are indeed spectra of certain
C*-algebras $A_\cosm$ and $A_\grav$, respectively, whereas the choices for the
algebras diverge in the literature. We decide now for all usual choices whether
the respective cosmological quantum configuration space is embedded into the
gravitational one. Typically, there is no embedding, but one can always get an
embedding by defining $A_\cosm := C^\ast(\sigma^\ast A_\grav)$, where $\sigma$
denotes the embedding between the classical configuration spaces. Finally, we
explicitly determine $C^\ast(\sigma^\ast A_\grav)$ in the homogeneous isotropic
case for $A_\grav$ generated by the matrix functions of parallel transports
along analytic paths. The cosmological quantum configuration space obtained
this way, equals the disjoint union of $\R$ and the Bohr compactification of
$\R$, appropriately glued together.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat