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Spin Foams with Matter: section 8 of Marcolli's paper, LQG/NCG roadmap, comments?

  1. May 10, 2010 #1

    marcus

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    Any comments you have on section 8 of http://arxiv.org/pdf/1005.1057
    are welcome and could be helpful.

    Section 8 "Spin Foams with Matter" begins on page 42 of Marcolli's latest paper.

    ==quote from ToC==
    8. Spin foams with matter: almost-commutative geometries 42
    8.1. The noncommutative geometry approach to the Standard Model 43
    8.2. Spectral triples and loop quantum gravity 45
    8.3. Spectral correspondences 46
    8.4. Future work
    ==endquote==

    Abstract and context for Marcolli's paper, Spin Foams and Noncommutative Geometry, is provided here
    https://www.physicsforums.com/showthread.php?t=401394 in the brief Oberwolfach thread.
     
    Last edited: May 10, 2010
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  3. May 10, 2010 #2

    marcus

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    One practical consequence is that Caltech has joined the select list of North American institutions where a grad student has the chance of finding an advisor and doing research in LQG. There aren't many such places, so it adds intellectual degrees of freedom.

    As a basis for comment, I will copy excerpts from section 8.

    ==quote==
    One of the most appealing features of general relativity is its geometric nature. That is, in general relativity the gravitational force manifests as the evolution of the metric structure of spacetime itself. In contrast, quantum field theories are decidedly non-geometric, with their dynamical variables being located in an abstract Hilbert space and interacting according to various representation-theoretic data that specify “particles.”

    Traditionally, one places quantum field theories on a background spacetime M by postulating the existence of a bundle structure over M. In this way, one creates an a priori distinction between the base manifold and fibers over it. The former is a geometric object, invariant under diffeomorphisms, while the latter are quantum field-theoretic, and invariant under gauge transformations.

    While this is more or less the most straightforward way of combining these two theories into one with the desired symmetry group C(M,G) × Diff (M), in the end what we have is a rather unmotivated and inelegant fusion.

    The idea that noncommutative geometry could provide a purely geometric interpretation for quantum field theories goes back to the beginnings of the former subject. Since noncommutative geometry gives us access to more general spaces beyond our ordinary “commutative manifolds,” the hope is that we could find some noncommutative space X such that our quantum field theory is given by the evolution of the geometry on this space, just as general relativity is a theory of the evolution of the geometry of a commutative manifold M.

    Quickly summarizing the current state of the art on this approach, we will simply say that this hope was indeed born out. In [30], Chamseddine, Connes, and Marcolli were able to reproduce the Standard Model minimally coupled to gravity and with neutrino mixing in a fully geometric manner—that is, as a theory of pure gravity on a suitable noncommutative space. This space is a product of an ordinary four-dimensional spacetime manifold with a small noncommutative space, which is metrically zero-dimensional but K-theoretically six-dimensional, and which accounts for the matter content of the particle physics model.

    In particular, the analogue of the diffeomorphism group for the noncommutative space in question reproduces the desired symmetry structure C(M,G)×Diff(M), with G = SU(3) × SU(2) × U(1) as desired.

    The elegant success of noncommutative-geometry techniques in coupling quantum field-theoretic matter to classical spacetime geometry then suggests a possible approach for doing the same with the quantum spacetime geometry of loop quantum gravity. In what follows, we give a brief flavor of how gauge theories on a classical manifold are constructed in the framework of noncommutative geometry, before surveying existing work on incorporating the spin networks and foams of loop quantum gravity into this same framework. Once we have an idea of how quantum spacetime and matter are separately accounted for by noncommutative geometry, we suggest an approach to combining them, thus adding matter to loop quantum gravity and achieving a unified theory of quantum matter on quantum spacetime.
    ==endquote==
     
  4. May 10, 2010 #3
    Would a completely successful LQG + NCG be considered a TOE? Perhaps NCG can supply the lagrangian needed for chiral twists in LQG'-Bilson braiding.
     
  5. May 10, 2010 #4

    marcus

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    Nothing said about Bilson braiding---that might or might not turn out to be the right approach to realizing matter in Lqg. This is a different approach. Let's look at another passage of the Marcolli paper, starting on page 45:

    ==quote==
    In this way, our original hope of realizing particle physics as an entirely geometric phenomenon is borne out: the Standard Model Lagrangian has been reproduced as a natural spectral action over the specified noncommutative space.

    8.2. Spectral triples and loop quantum gravity.

    The Noncommutative Standard Model, despite its success, still produces an essentially classical conception of gravity, as seen by the Einstein–Hilbert action embedded in eq. (8.2). Indeed, the authors of [36] comment on this directly in the context of their discussion of the mass scale Λ, noting that they do not worry about the presence of a tachyon pole near the Planck mass since, in their view, “at the Planck energy the manifold structure of spacetime will break down and one must have a completely finite theory.”

    Such a view is precisely that embodied by theories of quantum gravity, including of course loop quantum gravity—a setting in which spin networks and spin foams find their home. The hope would be to incorporate such existing work toward quantizing gravity into the spectral triple formalism by replacing the “commutative part” of our theory’s spectral triple with something representing discretized spacetime. Seen from another point of view, if we can find a way of phrasing loop quantum gravity in the language of noncommutative geometry, then the spectral triple formalism provides a promising approach toward naturally integrating gravity and matter into one unified theory.

    This idea of expressing LQG in terms of noncommutative geometry has been investigated recently in a series of papers by Aastrup, Grimstrup, Nest, and Paschke [37, 38, 34, 35, 39, 40, 41, 42, 43, 44]. Their starting point is to construct a spectral triple from the algebra of holonomy loops. The interaction between this algebra and the spectral triple’s Dirac operator reproduces the Poisson bracket of both Yang–Mills theory and of the Ashtekar formulation of general relativity upon which LQG is based. Later papers illuminate the situation by making contact with the semiclassical limit, where they retrieve the Dirac Hamiltonian for fermions coupled to gravity in [44]. Their approach also resolves a long-standing obstruction to naïve transference of the LQG Hilbert space into a spectral triple: namely, that the Hilbert space in question is nonseparable, which creates problems for the spectral triple construction.

    ==endquote==

    The "authors of [36]" are Chamseddine and Connes. Here at PF Beyond forum we discussed some of Aastrup Grimstrup's work back in 2006-2007, like the paper that is Marcolli's reference [38]
    [38] J. Aastrup and J. M. Grimstrup, “Intersecting Connes noncommutative geometry with quantum
    gravity,” Int. J. Mod. Phys. A22 (2007) 1589, arXiv:hep-th/0601127.
    It seemed like a distant longshot then. I think the first Loops conference where Grimstrup gave a paper was Loops 2008 ("QG-squared" at Nottingham). Since then this approach to building matter into LQG has gradually become more visible. It looks completely distinct from Bilson braiding to me, though some subtle connection might eventually emerge.
     
    Last edited: May 10, 2010
  6. May 10, 2010 #5
    The two probably are distinct, the reason I suggest it is that
    what are elementary particles in NCG? There isn't a lagrangian derived for braiding in LQG. I'm suggesting that NCG could supply an interpretation and lagrangian.

    btw

    http://www.fuw.edu.pl/~jpa/qgqg3/JesperGrimstrup.pdf
     
  7. May 10, 2010 #6
    So to be clear: Whereas something like braid matter uses the mechanics of LQG itself to construct something that acts like matter, what these guys did is just show that they have a mathematically reasonable way of affixing matter content to "points" in LQG space by describing this matter using the formalism of the noncommutative standard model. Do I have that right?

    Two things that stand out to me:

    - This seems like extremely early-stage exploratory work. They say at the end:

    ...and say they want to explore exactly what that means in future work. In other words, it sounds like they have shown that their construction is mathematically sensible (which is exciting by itself) but they don't yet have any idea what their construction actually does, or if when you run the dynamics it still has any of the properties we want LQG to have. Again, correct?

    - This may not be a substantive criticism, but: I find it a little bit troubling that the construction is so incredibly pure-mathematics oriented. Vanilla LQG, or braid matter, or string theory we have some sort of story we can tell to explain to someone not familiar with the mathematical formalisms what the theory is "doing". You don't need to necessarily understand tensor algebra to "get" what is happening in GR or with kaluza-klein electromagnetics, you don't need to understand holonomy groups to understand basic spin network dynamics, you don't need to understand the horribly complicated math happening in string theory to sort of get how matter emerges from that theory. NCG, which is after all about rigorously describing unintuitive geometric structures, seems fairly resistant to intuitive explanations, and so when we wed NCG to spin networks we are combining one extremely abstract construct with another extremely abstract construct to produce something that lives way out in the land of pure math even by mathematical physics standards. I don't think I could explain what the "product M × F of a commutative spin manifold and a finite noncommutative space" means (maybe I'd have more luck if I understood spectral triples) in a sort of intuitive sense, or what justification we have for the attached noncommutative space, except that when we run the numbers it gives us the lagrangian we want. Can anyone? Now given if what I'm describing here is a problem it probably is more a problem with how the NCG theory is commonly explained and taught than a problem with the theory's fundamentals themselves, but I would worry that the high degree of abstraction and the resulting fact that you basically have to learn two relatively obscure mathematical branches and then run numbers to say much of anything about this theory could make it easy for big conceptual problems with the idea to linger unnoticed for awhile...

    Anyway it should be very interesting to see where future work in this direction goes. Are there signs any of the established people working in either lqg or ncg such as Smolin or Connes might try to work with this new construction?
     
  8. May 10, 2010 #7
    Aastrup and Grimstrup has had papers from 2006 but so far as I know, it hasn't gotten much traction (i.e from Smolin or Connes) -- there appears some differences in detail (i.e the hilbert space in this is separable vs non-separable in LQG)


    arXiv:hep-th/0601127


    Intersecting Connes Noncommutative Geometry with Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup
    (Submitted on 18 Jan 2006)

    Abstract: An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented.

    1. arXiv:1003.3802 [pdf, other]
    Title: On a Derivation of the Dirac Hamiltonian From a Construction of Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
    Comments: 13 pages, two figures.
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
    2. arXiv:0911.4141 [pdf, other]
    Title: Lattice Loop Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup
    Comments: 3 figures
    Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
    3. arXiv:0911.2404 [pdf, other]
    Title: Emergent Dirac Hamiltonians in Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke
    Comments: one figure
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
    4. arXiv:0907.5510 [pdf, other]
    Title: On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
    Comments: 31 pages, 10 figures
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
    5. arXiv:0902.4191 [pdf, other]
    Title: Holonomy Loops, Spectral Triples & Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
    Comments: 24 pages, 7 figures, based on talk given by J.M.G. at the QG2 conference, Nottingham, juli 2008; at the QSTNG conference in Rome in sept/oct 2008; at the AONCG conference, Canberra, dec. 2008
    Journal-ref: Class.Quant.Grav.26:165001,2009
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
    6. arXiv:0807.3664 [pdf, ps, other]
    Title: A new spectral triple over a space of connections
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
    Comments: 14 pages, 5 figures
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
    7. arXiv:0802.1784 [pdf, ps, other]
    Title: On Spectral Triples in Quantum Gravity II
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
    Comments: 43 pages, 1 figure
    Journal-ref: J.Noncommut.Geom.3:47-81,2009
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
    8. arXiv:0802.1783 [pdf, ps, other]
    Title: On Spectral Triples in Quantum Gravity I
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest
    Comments: 84 pages, 8 figures
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
     
  9. May 10, 2010 #8

    marcus

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    Astute ("sociological") question. I think it's clear that sociological cues are an important way we get to understand leading edge research.

    The big news from NCG 2006-2008 is their realizing the Standard Model geometrically. Constructing a model of spacetime inwhich the particles and forces of physics were engrained in the spacetime. Intrinsic to to it, built in.

    The names on the papers presenting that result were
    Chamseddine
    Connes
    Marcolli

    What do you mean by "established people", Coin? In 2008 after she and co-authors put the Standard Model into NC geometry, Marcolli took a tenured full professorship in the Math department at Caltech.

    Before that, from 2003-2008, she was a tenured associate professor at the Max Planck Institute for Mathematics at Bonn.

    She was born in November 1969, still only 40. To me she looks established. I rate Caltech Math even higher than Caltech Physics. I wish her well. Who knows? (I just looked up Alain Connes, he was born 1 April 1947. Great guy. Wish him well too.)
     
    Last edited: May 10, 2010
  10. May 10, 2010 #9
    Since Smolin et al aren't publishing papers on qg-qg as he did on lqg-verlinde perhaps that's a sociological cue?

    I know NCG predicts Higgs mass and SM lagrangians but does it also explain some of the experimentally unexplained parameters of the SM like masses and 3 generations? Does it offer a DM candidate?
     
  11. May 10, 2010 #10

    marcus

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    Coin, John Barrett is established. He runs the show at Nottingham. He directs a QG funding agency of the ESF (european science foundation). He has a prominent bunch of grad students and postdocs at Nottingham. He has Kirill Krasnov. Rovelli sends his PhDs to Nottingham to postdoc. Barrett organizes QG schools and organized Loops 2008. His group has supplied Rovelli's program with key results, proved key theorems. Barrett is a major LQG figure. ("barrett-crane spin foam"?)

    Barrett was already doing NC geometry in 2006. The first Connes paper achieving the Standard Model in NCG, it came out the same week at a paper by Barrett proving the same result.
    http://arxiv.org/abs/hep-th/0608221

    This indicates a major established LQG player is interested in NCG, to the point of nearly scooping a bigtime Connes result. Barrett also invited Chamseddine (Connes' co-author) to be a plenary speaker at Loops 2008. (officially known as the "QG-squared" conference). Barrett's ESF funding agency as well as supporting LQG research, has also funded NCG workshops and schools.

    I actually don't KNOW how close the links are. But I think there is more than a enough platform for Marcolli's gambit to take off from. If it is Nature's will that it be a fruitful line of research :-D

    Right now if you want to look at the sociology I think you have to look at what the people are doing (the very good ones) that were born 1965 or later, and also keep an eye on the funding sources and the hirings.
    LQG is in a phase of rapid growth. Many strong younger people, increasing output. New faculty hires in places you wouldn't think of like Sydney Australia, LSU Baton Rouge, Karlsruhe, Haverford. Thomas Thiemann now has his own LQG team at Erlangen, another new center. Daniele Oriti recently set up his own team at Potsdam.

    If you do a spires search with the obvious keywords you get lqg/sf publications by year that go
    https://www.physicsforums.com/showthread.php?p=2708501#post2708501

    2005 40
    ...
    ...
    2009 140
    For details see the post I linked to.
    If you know another field of fundamental physical theory with comparable growth over the same period, please let me know.
    If I wanted to estimate the future I would not look at what the people that an outsider happens to know are doing.
    I would look at what the first-rate younger people are doing: Laurent Freidel, Kirill Krasnov, Etera Livine, Eugenio Bianchi, Simone Speziale, Florian Girelli, Emanuele Alesci, Florian Conrady, Jon Engle,... too many to try to be complete. All these young people, a few already advising their own graduate students but many of them just beginning to publish on their own.
     
    Last edited: May 10, 2010
  12. May 10, 2010 #11

    atyy

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    How about via group field theory, the link is pretty close, don't you think?

    spin foam - gft - ncg

    spin foam - gft is linked by Reisenberger and Rovelli

    gft - ncg is linked by Girelli, Livine and Oriti
     
  13. May 10, 2010 #12

    marcus

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    Heh heh, Atyy we both know that you have a sharp eye and an impressive memory for the web of research. I defer to you about the LQG/NCG roadmap. Yes! Florian Girelli! I had forgotten his name. Recently hired at University of Sydney, which starts another seedling Lqg research center.
     
  14. May 11, 2010 #13
    Marcus/ensabah thanks for the background on the paper authors.
     
  15. May 12, 2010 #14
    what works needs to be completed in combining LQG + NCG and what would be the name of this newer synthesis.

    What are the unresolved issues currently LQG + NCG and do they affect previous results from either loop or ncg

    in LQG + NCG, what are elementary partices in terms of spin networks, spin foam.
    Does LQG + NCG role in derifiving the candidate Hamiltonian for dynamics.
     
  16. May 12, 2010 #15
    Last edited by a moderator: Apr 25, 2017
  17. May 12, 2010 #16

    marcus

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    A world map of LQG centers!
    I hadn't realized how many of the new generation of researchers have already gotten permanent faculty positions. Now there are way more universities (than there used to be or that I knew about) where a grad student has the chance of finding an advisor and doing LQG research.

    I like the world map visual, Francesca. I will add it to the list of handy links in the "Intro to LQG" thread.
    https://www.physicsforums.com/showthread.php?p=2714192#post2714192
     
  18. May 13, 2010 #17

    marcus

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    Marcolli came out with another paper today. Taken together with her recent Spinfoam/NCG paper, this makes it look to me as if she is leading her Caltech group in the direction of quantum cosmology.

    http://arxiv.org/abs/1005.2256
    The spectral action and cosmic topology
    Matilde Marcolli (Caltech), Elena Pierpaoli (USC), Kevin Teh (Caltech)
    (Submitted on 13 May 2010)
    "The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll parameters can be sensitive to the underlying cosmic topology. We explicitly compute the non-perturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the Poincaré dodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters and see we check that the resulting inflation model behaves in the same way as for a simply-connected spherical topology in the case of the quaternionic space and the Poincaré homology sphere, while it behaves differently in the case of the flat tori. We add an appendix with a discussion of the case of lens spaces."

    I'm hoping someone here will explain what nonperturbative means in this context, so I've highlighted it.
     
    Last edited: May 13, 2010
  19. May 24, 2010 #18

    marcus

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    Today a couple of new NCG papers came out, with a phenomenology angle. I put them on the bibliography thread and will get the abstracts here in case anyone wants to comment.

    http://arxiv.org/abs/1005.4276
    Gravitational Waves in the Spectral Action of Noncommutative Geometry
    William Nelson, Joseph Ochoa, Mairi Sakellariadou
    15 pages, 3 figures
    (Submitted on 24 May 2010)
    The spectral triple approach to noncommutative geometry allows one to develop the entire standard model (and supersymmetric extensions) of particle physics from a purely geometry stand point and thus treats both gravity and particle physics on the same footing. The bosonic sector of the theory contains a modification to Einstein-Hilbert gravity, involving a nonconformal coupling of curvature to the Higgs field and conformal Weyl term (in addition to a nondynamical topological term). In this paper we derive the weak field limit of this gravitational theory and show that the production and dynamics of gravitational waves are significantly altered. In particular, we show that the graviton contains a massive mode that alters the energy lost to gravitational radiation, in systems with evolving quadrupole moment. We explicitly calculate the general solution and apply it to systems with periodically varying quadrupole moments, focusing in particular on the the well know energy loss formula for circular binaries.

    http://arxiv.org/abs/1005.4279
    Constraining the Noncommutative Spectral Action via Astrophysical Observations
    William Nelson, Joseph Ochoa, Mairi Sakellariadou
    5 pages
    (Submitted on 24 May 2010)
    The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. Thus, noncommutative geometry provides a geometric interpretation of particle physics coupled to curvature. In this letter we use observations of pulsar timings, assuming that no deviation from General Relativity has been observed, to constrain the gravitational sector of this theory. Thus, we directly constrain noncommutative geometry, a potential grand unified theory of physics, via astrophysical observations. Whilst the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from General Relativity in other settings and are likely to be further constrained by future observations.
     
    Last edited: May 24, 2010
  20. Jul 26, 2010 #19

    marcus

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    Re: LQG map

    That map is a really nice information resource, Francesca! I just updated the list of selected Lqg links here:
    https://www.physicsforums.com/showthread.php?p=2812996#post2812996
    and included your map.

    There is also a list of LQG researchers worldwide in Wikipedia which I think may be in part your doing. Potential advisors for someone who wants to do a PhD thesis in the field.
     
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  21. Jul 27, 2010 #20
    What's the status in NCG concerning the Higgs mass? The last model I've seen predicted a mass around 170 GeV, which is excluded by the Tevatron. How rigid is the Higgs mass prediction in Connes' model?
     
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