I have been working on a model of quantum gravity in which GR is formulated in the language of Quantum Mechanics .The latest version can be downloaded from the link below. Kindly peruse through to see if it meets the criteria of a self consistent theory.
No. A Hamiltonian formulation means a space of states and operators that act on them. In particular a quantized formulation means that it's possible to define a measure on the space of states, that describes geometries that do not solve Einstein's equations of motion-expressed in Hamiltonian form. That's what quantization means. There's no hint of such properties here.
A graviton is the 1-particle state of the field defined by the metric, that's all. This field theory is a gauge theory, with the diffeomorphism group as gauge group.
While GR is the classical limit of gravity, it's not at all clear of what quantum field theory it is the limit. A major problem is the generic appearance of black hole states, that describe, classically, causally disconnected regions of spacetime. A quantum theory of gravity must be able to resolve such singularities. In particular, point-like objects, of finite mass, would be naked singularities. That's one way of realizing that objects more complicated than points must describe the dynamics of gravity.
Thank you Stam for taking your time to answer the question. From your statement " A graviton is the 1-particle state of the field defined by the metric, that's all. " I can tell that you are applying the standard model concept of graviton to interpret the Nexus Paradigm graviton . The graviton in the Nexus Paradigm has properties that differ from those of the standard model graviton. It has also been shown that in the Nexus Paradigm there are no singularities you mention (kindly read the references provided in the paper ).
Stam Nicolis I have attached a version that includes the Hamiltonian equations and the commutation rules
Thank you Thierry for your time and suggestion that physics should be interpreted from a physics stand point. The Nexus graviton induces constant rotational motion on any test particle embedded within it's radius of action just as you point out that aspects of Gravitomagnetism should be found in quantum gravity. Dark matter is a manfestation of this Gravitomagnetic aspect of quantum gravity.
Any quantum theory of gravity, describes gravitons in the semi-classical limit-that's a standard consistency check of the formalism. In addition to that, it has to describe other spacetime geometries.
Singularities aren't removed-they're resolved-and must reappear in the classical limit. The proposal presented doesn't seem to do this.
Okay Stam why are you adamant that singularities aren't removed? GR is an incomplete theory and that was well understood from its inception when singularities arose alongside with the problem of energy conservation. Again the graviton you are alluding to is the SM graviton and not the Nexus graviton. The Nexus graviton is not a messenger particle but an atom of four space that can expand or contract. It's radius depends on its quantum state and can assumes scales ranging from the Planck four length to the Hubble four radius . Gravitational-waves arise in this paradigm in much the same way as sound is generated in matter.
http://www.worldscientific.com/doi/abs/10.1142/S0218271817500201?journalCode=ijmpd
Two observations currently in progress are likely to confirm predictions of the Nexus Paradigm. These are the LIGO Collaboration and the Event Horizon Telescope. Nexus predicts that all mergers of BHs will occur at speeds slightly above half light speed with low mass BH mergers occurring at almost exactly c/2. Simulations using GR predict 0.4c and those using Post Parameterized Newtonian (PPN) calculations predict 0.5c. PPN is not appropriate in the strong gravity regime of BHs.
The silhouette of Sgr A* is predicted to be 26 micro arcseconds in the Nexus Paradigm whereas GR predicts 52 micro arcseconds. Previous observations have already shown that the shadow must be less than 37 micro arcseconds.
https://en.m.wikipedia.org/wiki/Sagittarius_A*
The statement that the description proposed has anything to do with quantum gravity is incorrect. The reason is that how a classical gravitational wave induces transitions between quantum states isn't under control. The transition amplitudes aren't ell-defined.
Insofar as the ``Nexus graviton'' is a solution of Einstein's equations, it is a classical background and doesn't imply anything about quantum effects.
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