Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-compact groups, tensor operators and applications to quantum gravity   This work focuses on non-compact groups and their applications to quantum
gravity, mainly through the use of tensor operators. First, the mathematical
theory of tensor operators for a Lie group is recast in a new way which is used
to generalise the Wigner-Eckart theorem to non-compact groups. The result
relies on the knowledge of the recoupling theory between finite-dimensional and
infinite-dimensional irreducible representations of the group; here the
previously unconsidered cases of the 3D and 4D Lorentz groups are investigated
in detail. As an application, the Wigner-Eckart theorem is used to generalise
the Jordan-Schwinger representation of SU(2) to both groups, for all
representation classes. Next, the results obtained for the 3D Lorentz group are
applied to (2+1) Lorentzian loop quantum gravity to develop an analogue of the
well-known spinorial approach used in the Euclidean case. Tensor operators are
used to construct observables and to generalise the Hamiltonian constraint
introduced by Bonzom and Livine (2012) for 3D gravity to the Lorentzian case.
The Ponzano-Regge amplitude is shown to be a solution of this constraint by
recovering the (opportunely generalised) Biedenharn-Elliott relations. Finally,
the focus is shifted on the intertwiner space based on SU(2) representations,
widely used in loop quantum gravity. When working in the spinorial formalism,
it has been shown that the Hilbert space of n-valent intertwiners with fixed
total area is a representation of U(n). Here it is shown that the full space of
all n-valent intertwiners forms an irreducible representation of the
non-compact group SO*(2n). This fact is used to construct a new kind of
coherent intertwiner state (in the sense of Perelomov). Hints of how these
coherent states can be interpreted in the semi-classical limit as convex
polyhedra are provided.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat