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

In summary, the construction of LQG involves determining the dynamics, which can be done through a Hamiltonian constraint or a spin-foam formalism. However, there is no consensus on how to implement the dynamics, leading to multiple ideas but no agreement. A new symmetric Hamiltonian constraint operator has been proposed for LQG, which is well defined and diffeomorphism covariant. This operator also has a less ambiguous construction and can be applied to the symmetric model of loop quantum cosmology.
  • #1
palmer eldtrich
46
0
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?
 
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  • #2
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)
 

1. What is loop quantum gravity dynamics?

Loop quantum gravity dynamics is a theoretical framework in physics that attempts to reconcile general relativity and quantum mechanics. It proposes that space and time are composed of tiny, indivisible units called "loops" and that the laws of physics emerge from the interactions between these loops.

2. How does loop quantum gravity dynamics differ from other theories of quantum gravity?

Unlike other theories, loop quantum gravity dynamics does not assume that space and time are continuous. Instead, it describes them as discrete and quantized. This allows for a more consistent and mathematically well-defined approach to understanding the universe at the smallest scales.

3. What are the main challenges facing loop quantum gravity dynamics?

One of the main challenges is the development of a consistent and testable mathematical framework for the theory. Another challenge is reconciling it with other well-established theories, such as general relativity and quantum field theory.

4. How does loop quantum gravity dynamics explain the phenomenon of gravity?

In loop quantum gravity dynamics, gravity is described as the curvature of space and time caused by the interactions between the loops. This curvature is what we experience as the force of gravity. Loop quantum gravity dynamics also predicts that gravity is quantized, meaning it exists in discrete units.

5. What are some potential applications of loop quantum gravity dynamics?

Loop quantum gravity dynamics has the potential to provide a more complete and unified understanding of the laws of physics at both the smallest and largest scales. It could also help to explain the origins of the universe and provide insights into the behavior of black holes and other extreme objects in space.

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