# Signs of a Loop QG Wunderjahr

1. Jul 24, 2010

### marcus

LQG research is having what looks like a "heyday". A rush of papers that fit the various pieces of the puzzle together. See what you think. One sign is the series of papers this year from just one author and collaborators.
(PF posters who are more on the inside of the LQG program---having published papers related to these---may want to comment from a different perspective. This is a look from the outside.)

Loops 2011 conference will be in Madrid. I suppose that will be where all this development is displayed in some sort of order and we will see what has been accomplished. Right now it is difficult to integrate into a clear picture.

March:
http://arxiv.org/abs/1003.3483
Towards Spinfoam Cosmology
Eugenio Bianchi, Carlo Rovelli, Francesca Vidotto
8 pages

April:
http://arxiv.org/abs/1004.1780
A new look at loop quantum gravity
Carlo Rovelli
15 pages, 5 figures

May:
http://arxiv.org/abs/1005.0764
Face amplitude of spinfoam quantum gravity
Eugenio Bianchi, Daniele Regoli, Carlo Rovelli
5 pages, 2 figures

May:
http://arxiv.org/abs/1005.0817
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
Emanuele Alesci, Carlo Rovelli
24 pages

May:
http://arxiv.org/abs/1005.2927
On the geometry of loop quantum gravity on a graph
Carlo Rovelli, Simone Speziale
6 pages. 1 figure

May:
http://arxiv.org/abs/1005.2985
Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
Carlo Rovelli, Matteo Smerlak
4 pages

June:
http://arxiv.org/abs/1006.1294
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
You Ding, Carlo Rovelli
11 pages

2. Jul 24, 2010

### marcus

I will put in the abstract summaries for these papers and see what if anything takes shape from looking at the whole bunch.

March:
http://arxiv.org/abs/1003.3483
Towards Spinfoam Cosmology
We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.

April:
http://arxiv.org/abs/1004.1780
A new look at loop quantum gravity
I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.

May:
http://arxiv.org/abs/1005.0764
Face amplitude of spinfoam quantum gravity
The structure of the boundary Hilbert-space and the condition that amplitudes behave appropriately under compositions determine the face amplitude of a spinfoam theory. In quantum gravity the face amplitude turns out to be simpler than originally thought.

May:
http://arxiv.org/abs/1005.0817
A regularization of the hamiltonian constraint compatible with the spinfoam dynamics
We introduce a new regularization for Thiemann's Hamiltonian constraint. The resulting constraint can generate the 1-4 Pachner moves and is therefore more compatible with the dynamics defined by the spinfoam formalism. We calculate its matrix elements and observe the appearence of the 15j Wigner symbol in these.

May:
http://arxiv.org/abs/1005.2927
On the geometry of loop quantum gravity on a graph
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

May:
http://arxiv.org/abs/1005.2985
Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
The thermal time hypothesis has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we use the notion of thermal time to study thermal equilibrium on stationary spacetimes. Notably, we show that the Tolman-Ehrenfest effect (the variation of temperature in space so that $$T\sqrt{g_{00}}$$ remains constant) can be reappraised as a manifestation of this fact: at thermal equilibrium, temperature is locally the rate of flow of thermal time with respect to proper time - pictorially, "the speed of (thermal) time". Our derivation of the Tolman-Ehrenfest effect makes no reference to the physical mechanisms underlying thermalization, thus illustrating the import of the notion of thermal time.

June:
http://arxiv.org/abs/1006.1294
Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.

3. Jul 24, 2010

### marcus

Looking this over, some ideas (some vague, some less vague) come to mind.

One is the importance of the graph Hilbert space HΓ. All the quantum states of geometry with a given graph Γ underlying them, defined in the April paper. A graph is a simple object, not as simple as an integer but still fairly simple. A finite set of nodes and links, plus s(l) and t(l) directories that tell the source and target of each link l.

Another is the idea that restricting to states based on a particular graph or a set of graphs can serve as a truncation. We are looking at a possible option for a type of effective field theory with a type of cut-off that is not necessarily an energy or a momentum (not a quantity defined in some fixed reference).
Basically one wants to be able to calculate as if in perturbative mode, but without a stock default geometry to fall back on. Strategies for organizing approximation. Think of including more and more complicated graphs, increased numbers of nodes and links. I don't wish to give the impression that this is new or restricted to LQG!

Another salient idea here is the boundary Hilbert space. Picture a 4D spacetime region with a 3D boundary. Specifying the geometry on the boundary restricts the 4D geometry inside. This was the approach used to extract the LQG graviton propagator. The graviton is an idealization that needs to live in flat space, and such-like ideal venues, in order to be well-defined. The difficulty in getting a LQG graviton is you have to nail down the geometry to be flat---even though the theory uses no default background. This was done by restricting the boundary.

Another role the boundary plays is in giving physical meaning to the spin-foam path integral. A spin-foam can be seen as a "history" or way of getting from an initial spin-network to a final spin-network---summing over histories yields an amplitude of going from one 3D geometry to another 3D geometry. The initial and final 3D geometries form a boundary.

Another idea is the importance of cosmology for testing. The most accessible predictions based on LQG seem to concern the power spectrum and polarization of the cosmic microwave Background. This has been discussed a lot recently in papers by Aurelian Barrau and co-authors. The restricting assumptions of Loop cosmology are being relaxed so that the full LQG can be applied to cosmology, and thereby be tested.
Happily enough, Aurelien Barrau just presented a talk about testing LQG predictions on the microwave Background, to the ICHEP in Paris.
The importance of early universe cosmology to the overall LQG program is reflected in the above-listed March paper Towards Spinfoam Cosmology.

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Last edited: Jul 24, 2010