Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The length operator in Loop Quantum Gravity   The dual picture of quantum geometry provided by a spin network state is
discussed. From this perspective, we introduce a new operator in Loop Quantum
Gravity - the length operator. We describe its quantum geometrical meaning and
derive some of its properties. In particular we show that the operator has a
discrete spectrum and is diagonalized by appropriate superpositions of spin
network states. A series of eigenstates and eigenvalues is presented and an
explicit check of its semiclassical properties is discussed.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat