Our picks for first quarter 2012 MIRS (online QG seminar talks)

[marcus]

Which talks' input will contribute most to future research in Loop-and-allied quantum gravity?
Since the poll is multiple choice, it's possible to vote for several, if you choose. Abstract summaries follow in the next post.

PIRSA talks are online video. The ILQGS links are to the slides PDF. To get the online audio, replace .pdf by .wav in the URL. You will then be able to listen to the talk while you scroll through the slides.

ILQGS Sept. 20 http://relativity.phys.lsu.edu/ilqgs/puchta092011.pdf
The Feynman diagramatics for the spin foam models
Jacek Puchta, University of Warszaw

PIRSA Sept. 21 http://pirsa.org/11090125/
Loop Gravity as the Dynamics of Topological Defects
Eugenio Bianchi, Perimeter Institute

ILQGS Oct. 18 http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf
Inhomogeneous loop quantum cosmology
William Nelson, PennState

ILQGS Nov. 1 http://relativity.phys.lsu.edu/ilqgs/koslowski110111.pdf
Shape dynamics
Tim Koslowski, Perimeter Institute

ILQGS Nov. 15 http://relativity.phys.lsu.edu/ilqgs/engle111511.pdf
Plebanski sectors of the new spin foam models
Jonathan Engle, Florida Atlantic Univesrity

PIRSA Dec. 7 http://pirsa.org/11120050/
Canonical Time Evolution in Simplicial Gravity
Philipp Hoehn, Utrecht to Perimeter Institute

PIRSA Jan. 11 http://pirsa.org/12010131/
Group Field Theory and Simplicial Path Integrals
Aristide Baratin, AEI

PIRSA Jan. 18 http://pirsa.org/12010115/
Scalar Perturbations in Loop Quantum Cosmology
Edward Wilson-Ewing, Marseille to LSU

PIRSA Feb. 1 http://pirsa.org/12020096/
Continuous Formulation of the Loop Quantum Gravity Phase Space
Jonathan Ziprick, Perimeter Institute

ILQGS Feb. 14 http://relativity.phys.lsu.edu/ilqgs/perini021412.pdf
Classical limit of spin foams on arbitrary triangulations
Claudio Perini, PennState

PIRSA Feb. 15 http://pirsa.org/12020088/
Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data
Frank Saueressig, Univ. Mainz

ILQGS Feb. 28 http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
Continuous formulation of the LQG phase space
Marc Geiller, Univ. Paris

PIRSA Feb. 29 http://pirsa.org/12020129/
Spinor Quantisation for Complex Ashtekar Variables
Wolfgang Wieland, Marseille

ILQGS Mar. 13 http://relativity.phys.lsu.edu/ilqgs/diazpolo031312.pdf
Black hole evaporation in LQG
Jacobo Diaz-Polo, LSU

ILQGS Mar. 27 http://relativity.phys.lsu.edu/ilqgs/perez032712.pdf
Black hole entropy in LQG: new insights from a local perspective
Alejandro Perez, Marseille=============
For reference, here's a link to 2011's 4th qtr MIP poll (MIP="Most Important Paper(s)" in the indicated field of research.) https://www.physicsforums.com/showthread.php?t=563724
This quarter, for a change we're considering online Recorded Seminar talks, instead of papers. So instead of MIP it's a MIRS poll.
For those unfamiliar with the online seminar series, PIRSA stands for "Perimeter Institute Recorded Seminar Archive" and ILQGS stands for "International Loop Quantum Gravity Seminar". The ILQGS is held at several locations simultaneously via teleconferencing connection.

 

[marcus]

This is intended as a semiannual poll ( twice a year, covering recorded seminar talks from the previous 6 months or so.)
Not all the talks are listed with abstracts at their respective sites, so where possible I'll retrieve the relevant abstract from the main source paper the talk is based on.

ILQGS Sept. 20 http://relativity.phys.lsu.edu/ilqgs/puchta092011.pdf
The Feynman diagramatics for the spin foam models
Jacek Puchta, University of Warszaw
[paper's abstract: Feynman diagrammatic approach to spin foams--"The Spin Foams for People Without the 3d/4d Imagination" could be an alternative title of our work. We derive spin foams from operator spin network diagrams we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of Loop Quantum Gravity. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes that should be used in the spin foam theories of LQG. Within this class, our diagrams are just equivalent to the spin foams. The advantage, however, in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit visualization of the corresponding spin foams. The spin network diagram operators and amplitudes are consistently defined on their own. Each diagram encodes all the combinatorial information. We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli's surface amplitudes as well as of the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well as other possible models. The diagrams are also compatible with the structure of the LQG Hamiltonian operators, what is an additional advantage. Finally, a scheme for a complete definition of a spin foam theory by declaring a set of interaction vertices emerges from the examples presented at the end of the paper.]

PIRSA Sept. 21 http://pirsa.org/11090125/
Loop Gravity as the Dynamics of Topological Defects
Eugenio Bianchi, Perimeter Institute
A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects.

ILQGS Oct. 18 http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf
Inhomogeneous loop quantum cosmology
William Nelson, PennState
[abstract of related talk based on the same research (invited talk to be given by Nelson's co-author Ivan Agullo at the April meeting of the APS): Beyond the standard inflationary paradigm--The inflationary paradigm provides a compelling argument to account for the origin of the cosmic inhomogeneities that we observe in the CMB and galaxy distribution. In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises, and a clarification of what the trans-Planckian problems are and what they are not. In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles employed here.]

ILQGS Nov. 1 http://relativity.phys.lsu.edu/ilqgs/koslowski110111.pdf
Shape dynamics
Tim Koslowski, Perimeter Institute
[based on several papers including: Coupling Shape Dynamics to Matter Gives Spacetime--Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomorphisms and local spatial conformal transformations. In this paper we extend the construction of Shape Dynamics form pure gravity to gravity-matter systems and find that there is no obstruction for the coupling of gravity to standard matter. We use the matter gravity system to construct a clock and rod model for Shape Dynamics which allows us to recover a spacetime interpretation of Shape Dynamics trajectories.]

ILQGS Nov. 15 http://relativity.phys.lsu.edu/ilqgs/engle111511.pdf
Plebanski sectors of the new spin foam models
Jonathan Engle, Florida Atlantic University
[paper's abstract: A proposed proper EPRL vertex amplitude--As established in a prior work of the author, the linear simplicity constraints used in the construction of the so-called 'new' spin-foam models mix three of the five sectors of Plebanski theory, only one of which is gravity in the usual sense, and this is the reason for certain 'unwanted' terms in the asymptotics of the EPRL vertex amplitude as calculated by Barrett et al.
In the present paper, an explicit classical discrete condition is derived that isolates the desired gravitational sector, which we call (II+), following other authors. This condition is quantized and used to modify the vertex amplitude, yielding what we call the 'proper EPRL vertex amplitude.' This vertex still depends only on standard SU(2) spin-network data on the boundary, is SU(2) gauge invariant, and is linear in the boundary state, as required. In addition, the asymptotics now consist in the single desired term of the form e^iS_Regge, and all degenerate configurations are exponentially suppressed.]

PIRSA Dec. 7 http://pirsa.org/11120050/
Canonical Time Evolution in Simplicial Gravity
Philipp Hoehn, Utrecht to Perimeter Institute
[paper's abstract: Canonical simplicial gravity--A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the covariant formulation following directly from the action. We apply this formalism to simplicial gravity and (Euclidean) Regge calculus, in particular. A discrete forward/backward evolution is realized by gluing/removing single simplices step by step to/from a bulk triangulation and amounts to Pachner moves in the triangulated hypersurfaces. As a result, the hypersurfaces evolve in a discrete `multi-fingered' time through the full Regge solution. Pachner moves are an elementary and ergodic class of homeomorphisms and generically change the number of variables, but can be implemented as canonical transformations on naturally extended phase spaces. Some moves introduce a priori free data which, however, may become fixed a posteriori by constraints arising in subsequent moves. The end result is a general and fully consistent formulation of canonical Regge calculus, thereby removing a longstanding obstacle in connecting covariant simplicial gravity models to canonical frameworks. The present scheme is, therefore, interesting in view of many approaches to quantum gravity, but may also prove useful for numerical implementations.]

PIRSA Jan. 11 http://pirsa.org/12010131/
Group Field Theory and Simplicial Path Integrals
Aristide Baratin, AEI
[paper's abstract: Group field theory and simplicial gravity path integrals--In a recent work, a dual formulation of group field theories as non-commutative quantum field theories has been proposed, providing an exact duality between spin foam models and non-commutative simplicial path integrals for constrained BF theories. In light of this new framework, we define a model for 4d gravity which includes the Immirzi parameter gamma. It reproduces the Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing models otherwise; in particular it does not require any rationality condition for gamma. We formulate the amplitudes both as BF simplicial path integrals with explicit non-commutative B variables, and in spin foam form in terms of Wigner 15j-symbols. Finally, we briefly discuss the correlation between neighboring simplices, often argued to be a problematic feature, for example, in the Barrett-Crane model.]

PIRSA Jan. 18 http://pirsa.org/12010115/
Scalar Perturbations in Loop Quantum Cosmology
Edward Wilson-Ewing, Marseille to LSU
We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology.

PIRSA Feb. 1 http://pirsa.org/12020096/
Continuous Formulation of the Loop Quantum Gravity Phase Space
Jonathan Ziprick, Perimeter Institute
We relate the discrete classical phase space of loop gravity to the continuous phase space of general relativity. Our construction shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. We resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise-flat geometry, showing that both geometries belong to the same equivalence class. We also establish a clear relationship between Regge geometries and the piecewise-flat spin foam geometries. All of this is based on arXiv:1110.4833.

ILQGS Feb. 14 http://relativity.phys.lsu.edu/ilqgs/perini021412.pdf
Classical limit of spin foams on arbitrary triangulations
Claudio Perini, PennState
[earlier paper's abstract: Emergence of gravity from spinfoams--We find a nontrivial regime of spinfoam quantum gravity that reproduces classical Einstein equations. This is the double scaling limit of small Immirzi parameter (gamma) and large spins (j), with physical area (gamma times j) constant. In addition to quantum corrections in the Planck constant, we find new corrections in the Immirzi parameter due to the quantum discreteness of spacetime. The result is a strong evidence that the spinfoam covariant quantization of general relativity possesses the correct classical limit.]

PIRSA Feb. 15 http://pirsa.org/12020088/
Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data
Frank Saueressig, Univ. Mainz
The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In particular the spectral dimension, which measures the return probability of a fictitious diffusion process on space-time, provides a valuable probe which is easily accessible both in the continuum functional renormalization group and discrete Monte Carlo simulations of the gravitational action. In this talk, I will give a detailed exposition of the fractal properties associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). Comparing these continuum results to three-dimensional Monte Carlo simulations, we demonstrate that the resulting spectral dimensions are in very good agreement. This comparison also provides a natural explanation for the apparent conflicts between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.

ILQGS Feb. 28 http://relativity.phys.lsu.edu/ilqgs/geiller022812.pdf
Continuous formulation of the LQG phase space
Marc Geiller, Univ. Paris
[paper's abstract: Continuous formulation of the Loop Quantum Gravity phase space--
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux variables. Our construction shows that the fluxes depend on the three-geometry, but also explicitly on the connection, explaining their non commutativity. It also clearly shows that the flux variables do not label a unique geometry, but rather a class of gauge-equivalent geometries. This allows us to resolve the tension between the loop gravity geometrical interpretation in terms of singular geometry, and the spin foam interpretation in terms of piecewise flat geometry, since we establish that both geometries belong to the same equivalence class. This finally gives us a clear understanding of the relationship between the piecewise flat spin foam geometries and Regge geometries, which are only piecewise-linear flat: While Regge geometry corresponds to metrics whose curvature is concentrated around straight edges, the loop gravity geometry correspond to metrics whose curvature is concentrated around not necessarily straight edges.]

PIRSA Feb. 29 http://pirsa.org/12020129/
Spinor Quantisation for Complex Ashtekar Variables
Wolfgang Wieland, Marseille
During the last couple of years Dupuis, Freidel, Livine, Speziale and Tambornino developed a twistorial formulation for loop quantum gravity.
Constructed from Ashtekar--Barbero variables, the formalism is restricted to SU(2) gauge transformations.
In this talk, I perform the generalisation to the full Lorentzian case, that is the group SL(2,C).
The phase space of SL(2,C) (i.e. complex or selfdual) Ashtekar variables on a spinnetwork graph is decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a clean derivation of the solution space of the reality conditions of loop quantum gravity.
Key features of the EPRL spinfoam model are perfectly recovered.
If there is still time, I'll sketch my current project concerning a twistorial path integral for spinfoam gravity as well.

ILQGS Mar. 13 http://relativity.phys.lsu.edu/ilqgs/diazpolo031312.pdf
Black hole evaporation in LQG
Jacobo Diaz-Polo, LSU
[paper's abstract:Probing Loop Quantum Gravity with Evaporating Black Holes--
This letter aims at showing that the observation of evaporating black holes should allow distinguishing between the usual Hawking behavior and Loop Quantum Gravity (LQG) expectations. We present a full Monte-Carlo simulation of the evaporation in LQG and statistical tests that discriminate between competing models. We conclude that contrarily to what was commonly thought, the discreteness of the area in LQG leads to characteristic features that qualify evaporating black holes as objects that could reveal quantum gravity footprints.]

ILQGS Mar. 27 http://relativity.phys.lsu.edu/ilqgs/perez032712.pdf
Black hole entropy in LQG: new insights from a local perspective
Alejandro Perez, Marseille
[paper's abstract: A local first law for black hole thermodynamics--We first show that stationary black holes satisfy an extremely simple local form of the first law ∂ E=κ(l) ∂ A/(8 π) where the thermodynamical energy E=A/(8π l) and (local) surface gravity κ(l)=1/l, where A is the horizon area and l is a proper length characterizing the distance to the horizon of a preferred family of local observers suitable for thermodynamical considerations. Our construction is extended to the more general framework of isolated horizons. The local surface gravity is universal. This has important implications for semiclassical considerations of black hole physics as well as for the fundamental quantum description arising in the context of loop quantum gravity.]
NOTE the first 6 minutes of the Perez audio are spoiled by noise so I would advise dragging the time button to around 6:00 or 6:30 when you start it. This corresponds to around the slide numbered (2). The first part of the talk is a review, so missing the first few minutes need not be critical.

 

[marcus]

Already we have 3 respondents to the poll, and I just barely got through editing a final copy of the abstracts! Thanks for the response. I learn from seeing other's perspective and what others find the most promising lines of research. Hopefully before long we'll see a bunch of different viewpoints represented.

 

[MTd2]

I voted for things that look like non mainstream and weird as possible. LQG and its friends are almost mainstream.

I mean, if nothing seems to be working, at least it feels good to be underground or counter-culture! And shape dynamics has a preferential foliation, which gives me hope to use it as a way to build a FTL spacecraft someday. I mean, if you are bound to a foliation, you won't violate causality no matter how fast you go, you have just to find a warp mechanism.

 

[MTd2]

I am pretty sure marcus answered me and the post stayed long enough to not allow it being deleted. Is there a problem with PF forum's server?

 

[marcus]

I am pretty sure marcus answered me and the post stayed long enough to not allow it being deleted. Is there a problem with PF forum's server?

Hi MTd2, I didn't think it was appropriate so I deleted my own post! So there was no problem.

BTW I was glad to see that we both picked Frank Saueressig's PIRSA talk on the Asymptotic Safe approach. For me Frank S. now seems a very effective spokesman for Safe QG, on par with Reuter. He is also making strong progress in research. He has the advantage of being young, in the normally best years. People should watch that video!

He gives a fast introduction to what Safe QG is, in the first part, and why it may be true to nature---it would be a good introduction for anyone who is unfamiliar and wants to find out: well-organized and clear.

Then later in the talk he discusses the fact that dimensionality decays at small scale (not only in Safe but also in CDT and possibly Loop as well). We know this about Safe and CDT since 2005 (both Reuter and Loll gave plenary talks describing it at the Loops 2005 conference!).
Also as I think you know Steve Carlip has explained why there are even hints of this in *classical* GR. The classical theory, as he interprets it, goes some way towards supporting the decay that is found the non-string 4d quantum theories of geometry.

==================

Again I should stress, and I think you probably agree, that talk of Saueressig's was excellent! People should watch it if at all interested in Safe QG.

Also I think it's excellent that a talk can appeal to one person because of edgy "far-out" qualities and to someone else it can appeal because of solid mainstream-ness.

I think of Asym Safe QG as one of the most mainstream quantum extensions of GR. It may even be more widely accepted than Loop. (And the decay of dimensionality down from 4d to around 2d at small scale having been around since 2005 is no longer so shocking for me.)

=====================

EDIT: Oooops! I would have voted for Saueressig's talk but somehow omitted it when I was voting. I thought I had. It was definitely one of the best talks. I had too much to do yesterday and was rushing from one thing to another. I was glad to see that you voted for the talk. Not only insightful results and strong innovative research technique, but excellent presentation. He should probably become a "standard bearer" for the RG-flow approach to QG.

 

[marcus]

Sabine Hossenfelder discusses Safe QG starting on page 40 of her monograph on the minimal length scale http://arxiv.org/abs/1203.6191 (Living Reviews).
This theme (the limit to the resolution of structure that arises in various ways in several theoretical approaches to understanding spacetime) allows her to treat several major approaches on the same footing: String, Loop, Safe, and Spectral ("non-commutative geometry"). It's an important document. Evenhanded uncommitted but insightful style of the good phenomenologist.
She explains why you get a minimal scale of resolution in Safe QG too, as well as in other leading approaches.
Some people apparently don't like Reuter's name for it and have tried referring to it in other ways in their titles.
Cai Easson: "Higgs Boson in RG running Inflationary Cosmology" (1202.1285)

Donkin Pawlowski: "The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows" (1203.4207)

And for whatever reason, Saueressig himself does not headline the usual nomenclature in the title of his PIRSA talk:
"Fractal Space-times Under the Microscope: a RG View on Monte Carlo Data" (12020088)

It seems that if your title includes a hint like "cosmology", "spacetime" or "quantum gravity" so people know you are talking about geometry, then you do not need to use clunky language like *asymptotic safety* or *quantum Einstein gravity* (Weinbergly or Reuterian phrases).
You can just put in a tag like "RG running", "RG-flows" or "RG view", as these authors do, and people will know what you mean.

 

[marcus]

Diaz-Polo's talk is another important one because identifies a new way that Loop gravity can be tested by astrophysical observations. Distinctive radiation from evaporating black holes.

The paper it's based on is http://arxiv.org/abs/1109.4239

They find characteristic differences from the radiation spectrum Hawking predicted. Anything that opens a new route to testing QG is potentially significant.
================

Anybody with an interest in Loop should watch Wieland's talk. It's pretty amazing. I was impressed (I guess you can tell )
The paper it's based on is:
http://arxiv.org/abs/1107.5002
Twistorial phase space for complex Ashtekar variables
Wolfgang M. Wieland
(Submitted on 25 Jul 2011 (v1), last revised 24 Jan 2012 (this version, v2))
We generalise the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group SL(2,C). We show that the phase space for complex valued Ashtekar variables on a spinnetwork graph can be decomposed in terms of twistorial variables. To every link there are two twistors---one to each boundary point---attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.
18 pages, to appear in Classical and Quantum Gravity

 

[marcus]

So far Koslowski (Shape Dynamics) and Bianchi (Dynamics of Topological Defects) talks have taken the lead with Saueressig's talk on Asymptotic Safe QG running third.

6 people have voted, with a total of 16 votes cast. Thanks to all who have responded so far!

Interestingly, Bianchi's talk (in second place) is about a new way to formulate Loop geometry (curvature concentrated on the boundaries between flat cells, the socalled "defects" where cells join, so the geometry "lives" on these defects, so to speak, and the dynamics of the defects captures the whole story.) And this new formulation is drawn on in the research that both Ziprick and Geiller describe in their talks.

 

[marcus]

So far the poll is interesting for me partly because it goes against my personal assessment of where QG presently stands.
Of course we can't know the future, especially of research, so we can't tell what gambits/initiatives will pay off. But I have a strong hunch that Puchta's talk is the most breakthrough landmark one:

The Feynman diagrammatics for the spin foam models
http://relativity.phys.lsu.edu/ilqgs/puchta092011.pdf
http://relativity.phys.lsu.edu/ilqgs/puchta092011.wav

Of course I voted for several others besides, which I see as promising but secondary.
But Puchta's is my strong favorite. Maybe I will try to explain why that one stands out.
(Actually it would be interesting if some of the other respondents would explain their choices. MTd2 already has, which is a plus.)

The key thing--you may need to think about it some before you realize why it is so important--is that to each of a large class of spinfoams it associates a unique labeled graph. Each graph can be "contracted" to give the amplitude of that "path"---the amplitude associated with the original spinfoam jumps out, you don't have to dig for it.
Now in contrast to foams, graphs can be straightforwardly enumerated. I have not followed thru enough to be sure but it looks to me that this opens the door to a true path integral.

In other words you can choose two quantum states of geometry--Initial and Final geometries--each represented by a network graph. And you can generate by computer algorithm all the spinfoams* that evolve the geometry from one state to the other. And the process for generating each of those spinfoam "paths", that geometry could take, gives you an unique labeled operator graph associated with it---and the amplitude of the path jumps out at you (by a straightforward contraction of the labels along the graph.)

So you can sum the amplitudes of all the paths going from one geometric state to the other** and have a "sum over histories".

*of a large class which the Warsaw people think is big enough, this is a question that needs to be settled.
** at least up to some cutoff level of complexity, the ultimate convergence issue also needs to be settled.

I guess the basic point here is that you can describe each 2-complex by a graph. I think of that as non-trivial mathematically, something I did not expect. Graphs are combinatorially simpler than 2-complexes, and easier for a blind automata to enumerate systematically. The Warsaw people did something quite unexpected, and this stands out prominently.

 

[marcus]

To be more specific, here is the key passage from the Warsaw group's paper, page 2:

B. Our goal - the spin network diagrams
In the current paper we derive spin foams from operator spin network diagrams we introduce. Our diagrams are the spin network analogy of the Feynman diagrams. Their framework is compatible with the framework of LQG. For every operator spin network diagram we construct a corresponding operator spin foam. Admitting all the spin networks of LQG and all possible diagrams leads to a clearly defined large class of operator spin foams. In this way our framework provides a proposal for a class of 2-cell complexes used in the spin foam theories. Within this class, our diagrams are just equivalent to the spin foams.
The advantage in the diagram framework is, that it is self contained, all the amplitudes can be calculated directly from the diagrams without explicit constructing the corresponding spin foams. Indeed, the spin network diagram operators and amplitudes can be consistently defined on their own. Given a diagram the reconstruction of an operator spin foam itself is not necessary, because the diagram encodes all the information. And it is convenient, because using the diagrams is much simpler than using the spin foams, therefore one may call our framework the spin networks for people without the 3- and 4-dimensional space imagination.
We illustrate applications of our diagrams: we introduce a diagram definition of Rovelli’s surface amplitudes as well as the canonical transition amplitudes. Importantly, our operator spin network diagrams are defined in a sufficiently general way to accommodate all the versions of the EPRL or the FK model, as well other possible models. The diagrams are also compatible with the framework used in LQG to define the Hamiltonian operators, which is an additional advantage.
Our paper is organized as follows...​

The point is that from a given operator spin network, a labeled graph in other words, one can derive the (presumably unique) foam (i.e. labeled 2-complex) associated with it. And each operator spin network comes with a readily accessible probability amplitude.

So if all works out as they expect (it's new) they can enumerate all the graphs representing paths from Initial to Final geometry, and add up their amplitudes. Bingo, a path integral.

If you want to see the paper that Puchta's talk is based on, and that quoted here, you can simply google "arxiv feynman puchta" and get:
http://arxiv.org/abs/1107.5185
Feynman diagrammatic approach to spin foams
Marcin Kisielowski, Jerzy Lewandowski, Jacek Puchta

 

[marcus]

I got a PM that raised a question about William Nelson's talk the significance of which I ventured to discuss a little bit in Cosmology forum:
https://www.physicsforums.com/showthread.php?p=3842724#post3842724
So I will respond to the general thrust of the question here in case anyone else is interested.

The point is that based on some work by Ivan Agullo and Leonard Parker (Harvard Phd 1966?) some of the structure BEFORE inflation comes thru due to stimulated particle creation.
So inflation does not wipe the slate clean. The inflationary period (if it occurred as is commonly supposed) is, in a sense, transparent.

We can see (signs of) the density map of what came before.

This is of considerable interest to Loop cosmology researchers because what came before, a bounce and a brief period of naturally faster-than-exponential expansion (called "superinflation"), is of considerable interest to them.

So in the Loop case we may be able to see back before inflation. And Ivan Agullo was invited to give a talk about this at the April meeting of the American Physical Society.

 

[marcus]

I got a PM today that raised a question about William Nelson's talk the significance of which I ventured to discuss a little bit in Cosmology forum:
https://www.physicsforums.com/showthread.php?p=3842724#post3842724
So I will respond to the general thrust of the question here.

The point is that based on some work by Ivan Agullo and Leonard Parker (Harvard Phd 1966?) some of the structure BEFORE inflation comes thru due to stimulated particle creation.
So inflation does not wipe the slate clean. The inflationary period (if it occurred as is commonly supposed) is, in a sense, transparent.

We can see (signs of) the density map of what came before.

This is of considerable interest to Loop cosmology researchers because what came before, a bounce and a brief period of naturally faster-than-exponential expansion (called "superinflation"), is of considerable interest to them.

So in the Loop case we may be able to see back before inflation. And Ivan Agullo was invited to give a talk about this at the April meeting of the American Physical Society.
https://www.physicsforums.com/showthread.php?p=3842676#post3842676

 

[marcus]

A paper came out today by Agullo, Ashtekar, and Nelson that gives us something else to use in understanding William Nelson's talk. Because this paper had not come out yet, I used the abstract of a talk that Nelson's coauthor Ivan Agullo just gave a few days ago at the Atlanta meeting of the American Physical Society.
Now we have the paper itself and can do an update.
This is what we had earlier:

ILQGS Oct. 18 http://relativity.phys.lsu.edu/ilqgs/nelson101811.pdf
Inhomogeneous loop quantum cosmology
William Nelson, PennState
[abstract of related talk based on the same research (invited talk to be given by Nelson's co-author Ivan Agullo at the April meeting of the APS): Beyond the standard inflationary paradigm--The inflationary paradigm provides a compelling argument to account for the origin of the cosmic inhomogeneities that we observe in the CMB and galaxy distribution. In this talk we introduce a completion of the inflationary paradigm from a (loop) quantum gravity point of view, by addressing gravitational issues that have been open both for the background geometry and perturbations. These include a quantum gravity treatment of the Planck regime from which inflation arises, and a clarification of what the trans-Planckian problems are and what they are not. In addition, this approach provides examples of effects that may have observational implications, that may provide a window to test the basic quantum gravity principles employed here.]

Now in addition to that we have the actual A,A,and N paper:

http://arxiv.org/abs/1204.1288
Perturbations in loop quantum cosmology
Ivan Agullo, Abhay Ashtekar, William Nelson
(Submitted on 5 Apr 2012)
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, Quantum Gravity, phase of the universe. Here we describe how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB.
4 pages, ICGC (2011) Goa Conference proceedings

Nelson's talk had the same title as the paper Perturbations in loop quantum cosmology (which had not come out yet) and the talk was clearly based on it. But the talk is actually wide ranging and hits several different areas of investigation listed on one of his first slides:
*INFLATION (focus of Agullo's talk at aPS. the fact that pre-inflation inhomogeneities can persist even thru inflation)
*HAMILTONIAN PERTURBATIONS IN COSMOLOGY
*QFT IN QUANTUM (COSMOLOGICAL) SPACE-TIMES
*PERTURBATIONS IN LQC