Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergent $\tilde{Y}$-Map for a new covariant Loop Quantum Gravity
  formulation   The most important part of the new spin-foam loop quantum gravity formulation
is the map $Y$: $H^{SU(2)} \rightarrow H^{SL(2,C)}$. It was only recently shown
that the Y-Map is convergent in spite of the fact that the classical Peter-Weyl
theorem is not applicable to it, as Lorentz group is not compact. In this paper
we provide an alternative map $\tilde{Y}$. The $\tilde{Y}$ map has an advantage
of preserving the Lorentz covariance, which gets broken in the case of Y-Map.
The image of a new map $\tilde{Y}$ contains the weighted infinite sum of
$SL(2,C)$ matrix coefficients. The sum is convergent and its limit is the
square integrable functions of $SL(2,C)$ with the measure $L^2(g,
e^{-|Y|^2/\hbar}\eta(g) du \,dY )$ according to the Holomorphic
Huebschmann-Peter-Weyl theorem, which is applicable to the rational
representations of the non-unitary groups, particularly non-unitary finite
Lorenz representations. Since in LQG the unitary evolution is not mandatory as
it does not follow from the Wheeler-DeWitt dynamics equation, the choice of the
non-unitary representation is valid. As it was stated in the original LQG
formulation: "there is no sense in which conventional unitarity is necessary in
the theory".

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
18
The categories of this paper are: econ
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph