If LQG now satisfactory, how to add matter?

[marcus]

So what is responsible for the transmission of forces? There is no gauge particles now?

fields. I consider a field is a more general concept than particle.
(I mean something specific by particle. A particle is something that can be counted. One can say unambiguously how many there are. A field does not always resolve into a definite number of particles---it may depend on the viewpoint etc---but in come cases on a fixed background such as Minkowski space it may usefully be so treated.)

This is probably just a semantic misunderstanding. You know very well what you are talking about and you are not confused---but we could be using words differently. I believe that fields really exist and live in geometry (which is itself a field). I don't believe particles exist as a real part of my fundamental ontology---instead their fields exist. The appearance of a particle is just a temporary mathematical device for describing a field, which may or may not be appropriate in the given situation.

I'm not saying anything that is unusual or out of the mainstream, I hope! I vaguely recall someone, Feynman I think, remarking that an electron could be as big as the Empire State building in New York City. Because the building has a steel frame.

 

[marcus]

Actually, reading the paper, it seems the concept is not so hard --- after all, the current spinfoam incarnation is conceptually a quantum (i.e. linearly superposable) discretised geometry. As has been known for a while, on the classical level fermions + YM can be written as a theory of gauge strings connected by fermions; this paper I believe simply (!) implements that idea. Thus, particle states are localised --- but at the same time slightly delocalised --- to spacetime vertices, which means that at each vertex you get a set of fermion states (0, +/- or 2).

I'm not entirely sure at the moment what they mean by using the gravitational radiative corrections to generate the YM action, but I suspect they mean by a Einstein-KK-esque argument, on the quantum level.

I find all this development to be massively exciting, though in the end the proof will be in the form of concrete calculations (and of course, experimental verification of said calculations).

Genneth, I strongly agree. This year has been one of very rapid development in LQG. Probably the best overall perspective/review is the one I call "December 4707" to help me remember the arxiv tag:
http://arxiv.org/abs/1012.4707.

This review takes the contents of several interesting (series of) LQG papers, including the one you referred to, the Spinfoam Fermions paper, and puts them all together in a balanced coherent picture---with some motivation and history. December 4707 is the one thing I'm trying to find time to study in the midst of Holiday festivities.

In case anyone just dropped in, the Spinfoam Fermions paper is December 4719.
In other words http://arxiv.org/abs/1012.4719

 

[space_cadet]

fields. I consider a field is a more general concept than particle. (I mean something specific by particle. A particle is something that can be counted. One can say unambiguously how many there are. A field does not always resolve into a definite number of particles---it may depend on the viewpoint etc---but in come cases on a fixed background such as Minkowski space it may usefully be so treated.)

So what about wave-particle duality then? Also it is true that there is ambiguity in the definition of a particle, but there is also ambiguity in the definition of a field. That's what gauge and diffeomorphism invariance are all about, right?

This is probably just a semantic misunderstanding. You know very well what you are talking about and you are not confused---but we could be using words differently. I believe that fields really exist and live in geometry (which is itself a field). I don't believe particles exist as a real part of my fundamental ontology---instead their fields exist. The appearance of a particle is just a temporary mathematical device for describing a field, which may or may not be appropriate in the given situation.

Couldn't we switch the words "particle" and "field" in the above paragraph and still have it make sense? If you think about geometry, at a quantum level, you expect it to be discrete or at least not smoothly continuous ($$C^\infty$$). There should be all kinds of defects and singularities, and you might naturally want to designate such structures as "particles".

I'm not saying anything that is unusual or out of the mainstream, I hope! I vaguely recall someone, Feynman I think, remarking that an electron could be as big as the Empire State building in New York City. Because the building has a steel frame.

I don't get that last part.

To sum up, IMHO, you need both - fields and particles. Particles are what source fields and fields are what shuttle back and forth between particles helping them communicate. And in the end everything is geometry ;-) !

ps: I've been following this discussion and thought this might be a good time to jump in :-)

 

[marcus]

Always have to be careful with wikipedia, not the most authoritative source! however
http://en.wikipedia.org/wiki/Quantum_field_theory
"...Fermions, like the electron, can also be described as ripples/excitations in a field, where each kind of fermion has its own field. In summary, the classical visualisation of "everything is particles and fields," in quantum field theory, resolves into "everything is particles," which then resolves into "everything is fields." In the end, particles are regarded as excited states of a field (field quanta)..."

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime..."

 

[MTd2]

Well, by coupling fermions and YM fields now, LQG is done, right? Although, I wonder about the non gauge bosons...

 

[genneth]

Well, by coupling fermions and YM fields now, LQG is done, right? Although, I wonder about the non gauge bosons...

Actually, one might hope there aren't any. Renormalisation arguments show that plain ol' self-interacting bosons tend to have Landau poles, which strongly suggest that something (i.e. phase transition) must occur before the Planck scale. After all, the current dominant Higgs mechanism in electroweak breaking is just the simplest possible one of its type --- one could (and many have) plausibly imagine quite complicated bosonic structures which arise out of some higher energy phase transition instead. The only real constraint is that there should be a massless boson beforehand --- and Goldstone's theorem provides plenty of those in abundance.

 

[marcus]

The major QG story these days is the convergence of different approaches into a settled form of the theory. Satisfactory as theory-building goes, ready for testing.

Adding matter to the theory is an important step---earlier in this thread we mentioned the "Spinfoam Fermions" paper (http://arxiv.org/abs/1012.4719). Here is another piece of the puzzle. You may get the idea from the abstract that it is only about 3D gravity, but look at the conclusions. The authors' focus is on the merger of two research lines in the full 4D theory.

MTd2 spotted this one, and added it to the bibliography today.

http://arxiv.org/abs/1101.3524
The Hamiltonian constraint in 3d Riemannian loop quantum gravity
Valentin Bonzom, Laurent Freidel
(Submitted on 18 Jan 2011)
"We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of discrete geometries: it computes the extrinsic curvature from dihedral angles. The Wheeler-DeWitt equation takes the form of difference equations, which are actually recursion relations satisfied by Wigner symbols. On the boundary of a tetrahedron, the Hamiltonian generates the exact recursion relation on the 6j-symbol which comes from the Biedenharn-Elliott (pentagon) identity. This fills the gap between the canonical quantization and the symmetries of the Ponzano-Regge state-sum model for 3d gravity."

What we see happening on a lot of fronts is what could be called "tying up loose ends."

What has become the main LQG thrust (latest review paper: http://arxiv.org/abs/1012.4707 ) is not "derived" from anyone thing by some "quantization" procedure. It is a kind of synthesis inspired by several QG directions. So it is buttressed from several independent developments and an important one is the older Hamiltonian approach. That older program was never fully completed. So it looks like Bonzom Freidel are investigating how to complete it and how it will, when completed, support the prevaling spinfoam covariant approach.

 

[marcus]

To save the reader trouble, here is the portion of the conclusions of the Bonzom Freidel paper relevant to the 4D program:
==quote http://arxiv.org/abs/1101.3524 ==

...Our result shows that it is possible to identify very precisely the recurrence relations satisfied by spin foam amplitudes with a quantum implementation of the classical symmetries in loop quantum gravity. Thus, this suggests two ways to apply this programme to 4d LQG.

The first idea is to derive recurrence relations for the amplitudes of the most promising spin foam models, and then try to produce them from an operator in LQG. Since these models describe geometry with areas and normals to triangles, we expect the corresponding operator to produce both differences on spins and some differential parts on the normals.

The second idea is to first derive difference equations from an operator and then interpret them as recurrence relations for some spin foam models. Typically, our operator Hv,f has a natural generalization in 4d. ...
...
Ultimately, one may expect these two approaches to coincide. This is actually what we achieved in the present article on the 3d model.

In four dimensions, some preliminary results have been obtained in [6]. There the topological Ooguri model for BF theory is revisited by lifting the Hamiltonian we have just used here, H_v,f , to the boundary of a 4-simplex. Classically, this provides the phase space of 4d loop quantum gravity with a Hamiltonian dynamics which can be interpreted in terms of twisted geometries. In the spin network basis, the Wheeler-DeWitt equation gives recursion relations which are actually satisfied by the Wigner 15j-symbol. We expect to extend these ideas for more realistic spin foam models ...

More generally, the relation between spin foams and Hamiltonian dynamics is investigated in [6] in the large spin limit through difference equations on the 4-simplex amplitude. In 3d, such an equation is obviously the recursion relation (4) on the 6j-symbol, simplified in the asymtotics. Such equations give criteria to know whether a model is semi-classically approximated by some quantum Regge calculus. For instance, it is clear from these results that the (naive) proposal (89) is solved in the asymptotics by exponentials of i times the Regge action of the 4-simplex with quantized areas.
==endquote==

 

[MTd2]

The problems were solved with a restriction that was done on the phase space of LQG. This is funny considering Freidel's previous paper.

 

[marcus]

The problems were solved with a restriction that was done on the phase space of LQG. This is funny considering Freidel's previous paper.

More comment by MTd2 on this topic:
https://www.physicsforums.com/showthread.php?p=3092118#post3092118

Reminder about the particle concept when space is curved:

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime..."

The thread topic is ideas of how LQG can add matter. We already mentioned this December 2010 paper:

More on the including matter front. This was posted today:
http://arxiv.org/abs/1012.4719
Spinfoam fermions
Eugenio Bianchi, Muxin Han, Elena Magliaro, Claudio Perini, Carlo Rovelli, Wolfgang Wieland
8 pages
(Submitted on 21 Dec 2010)
"We describe a minimal coupling of fermions and Yang Mills fields to the loop quantum gravity dynamics. The coupling takes a very simple form."
...

For completeness, we should add a followup paper that appeared in January 2011 along the same lines:

http://arxiv.org/abs/1101.3264
Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions
Muxin Han, Carlo Rovelli
26 pages, 9 figures
(Submitted on 17 Jan 2011)
"We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravity-fermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for spinfoam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spinfoams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex."

 

[marcus]

How to add matter?

In view of everything we have been seeing happen in QG recently the question for 2011 does seem to boil down to the topic question of this thread: how to add matter?

I want to review the evidence (some quite recent and not yet covered in this thread) that this is the question that is "on everybody's mind" in the QG community.

This is interpretive, and I could be wrong. If you see a different prevailing focus in today's research, schools, workshops, conferences ...etc then please articulate it in opposition to my view.

I'll start reviewing the evidence and trying to integrate the different stuff we are seeing at this point, maybe tomorrow, or later this evening.

 

[atyy]

Try the last chapter of Hellman's thesis.

 

[marcus]

Atyy, thanks for the pointer. I will fetch your explanatory comment from the other thread and keep it in mind. What I'm thinking about now is my impression that a combined field of QG is taking shape consisting of maybe half-dozen different research lines. I quote from the
http://www.conferences.itp.phys.ethz.ch/doku.php?id=qg11:start
homepage of the June Zurich conference

Topics to be covered include:

• General quantum theory, relativistic quantum theory, emergence of space(-time)
• General quantum field theory, including deformations of QFTs
• QFT on curved and NC space-times
• Canonical quantum gravity and supergravity
• Regge calculus
• String theory and M-theory
• Loop gravity, spin foam
• Quantum cosmology

International Advisory Board

John Barrett
Harald Grosse
Hermann Nicolai
Carlo Rovelli
Roger Picken

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

The message of the conference seems to be that QG (quantum geometry/gravity) is a single field and that to the extent that your research is about QG you ought to know the other people and what they are doing, and how it might relate to what you do.
========================

This is still an indefinite thought on my part. I am not sure of it. I have the idea that what it means for the LQG people is they will now focus on the question how to add matter.

LQG already has a pretty strong hand in quantum cosmology. (both theory and phenomenology). But I have the expectation that the community is going to focus on adding matter. I'm not sure why I think that. Some hint of it in recent papers of Rovelli and of Barrett, perhaps.

I guess it is part of a natural process of consolidation where you build bridges to other research contingents that belong to the same field.

BTW John Baez is one of the Zurich speakers. (He's the one who called our attention to the conference.) Also Lance Dixon. Also Alain Connes.