Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Martin-Benito-Mena Marugan-Olmedo prescription for the
  Dapor-Liegener model of Loop Quantum Cosmology   Recently, an alternative Hamiltonian constraint for Loop Quantum Cosmology
has been put forward by Dapor and Liegener, inspired by previous work on
regularization due to Thiemann. Here, we quantize this Hamiltonian following a
prescription for cosmology proposed by Mart\'{\i}n-Benito, Mena Marug\'an, and
Olmedo. To this effect, we first regularize the Euclidean and Lorentzian parts
of the Hamiltonian constraint separately in the case of a Bianchi I cosmology.
This allows us to identify a natural symmetrization of the Hamiltonian which is
apparent in anisotropic scenarios. Preserving this symmetrization in isotropic
regimes, we then determine the Hamiltonian constraint corresponding to a
Friedmann-Lema\^itre-Robertson-Walker cosmology, which we proceed to quantize.
We compute the action of this Hamiltonian operator in the volume eigenbasis and
show that it takes the form of a fourth-order difference equation, unlike in
standard Loop Quantum Cosmology, where it is known to be of second order. We
investigate the superselection sectors of our constraint operator, proving that
they are semilattices supported only on either the positive or the negative
semiaxis, depending on the triad orientation. Remarkably, the decoupling
between semiaxes allows us to write a closed expression for the generalized
eigenfunctions of the geometric part of the constraint. This expression is
totally determined by the values at the two points of the semilattice that are
closest to the origin, namely the two contributions with smallest eigenvolume.
This is in clear contrast with the situation found for the standard Hamiltonian
of Loop Quantum Cosmology, where only the smallest value is free. This result
indicates that the degeneracy of the new geometric Hamiltonian operator is
equal to two, doubling the possible number of solutions with respect to the
conventional quantization considered until now.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn