What is the new Hamiltonian constraint operator for loop quantum gravity?

[palmer eldtrich]

A critique of LQG here:
"The next step in the construction of LQG is to decide what the dynamics are. Technically, this is done either (A) by choosing a "Hamiltonian constraint" in parallel with the Hamiltonian formulation of GR, or (B) in the spin-foam formalism, by postulating some sort of sum over histories assigning an action to each spin foam. It is here which we encounter the major problem: There is no agreement over how to implement the dynamics! There are many ideas, but no consensus on what to do.

Is this right and is it still the case?

 

[kodama]

New Hamiltonian constraint operator for loop quantum gravity
Jinsong Yang, Yongge Ma
(Submitted on 3 Jul 2015 (v1), last revised 17 Jul 2015 (this version, v2))
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method, so that its regulated version in the kinematical Hilbert space is diffeomorphism covariant and creates new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
Comments: 5 pages; a few modifications
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1507.00986 [gr-qc]
(or arXiv:1507.00986v2 [gr-qc] for this version)