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Most Influential Paper fourth quarter 2006

  1. Chamseddine, Connes and Marcolli

    33.3%
  2. Baratin and Freidel

    33.3%
  3. Wise

    33.3%
  4. Alexandrov, Buffenoir and Roche

    0 vote(s)
    0.0%
  5. Freidel, Kowalski-Glikman and Nowak

    0 vote(s)
    0.0%
  1. Dec 28, 2006 #1

    marcus

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    The following background independent QG preprints appeared October through December 2006. Which of these do you expect to have the greatest impact on future research?

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

    http://arxiv.org/abs/hep-th/0610241
    Gravity and the standard model with neutrino mixing
    Ali H. Chamseddine, Alain Connes, Matilde Marcolli
    71 pages, 7 figures

    "We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector."

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

    http://arxiv.org/abs/hep-th/0611042
    Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
    Aristide Baratin, Laurent Freidel
    28 pages, 7 figures

    "We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the symmetries of this Feynman graph spin foam model and give the gauge-fixing prescriptions. We also show that the gauge-fixed partition function is invariant under Pachner moves of the triangulation, and thus defines an invariant of four-dimensional manifolds. Finally, we investigate the algebraic structure of the model, and discuss its relation with a quantization of 4d gravity in the limit where the Newton constant goes to zero."

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

    http://arxiv.org/abs/gr-qc/0611154
    MacDowell-Mansouri gravity and Cartan geometry
    Derek K. Wise
    34 pages, 5 figures

    "The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous 'model spacetime', including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A 'Cartan connection' gives a prescription for parallel transport from one 'tangent model spacetime' to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as 'rolling' the model spacetime along physical spacetime. I explain Cartan geometry, and 'Cartan gauge theory', in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its recent reformulation in terms of BF theory, in the context of Cartan geometry."

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

    http://arxiv.org/abs/gr-qc/0612071
    Plebanski Theory and Covariant Canonical Formulation
    Sergei Alexandrov, Eric Buffenoir, Philippe Roche
    18 pages

    "We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed."

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

    http://arxiv.org/abs/hep-th/0612170
    From noncommutative kappa-Minkowski to Minkowski space-time
    Laurent Freidel, Jerzy Kowalski-Glikman, Sebastian Nowak
    6 pages

    "We show that free kappa-Minkowski space field theory is equivalent to a relativistically invariant, non local, free field theory on Minkowski space-time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent."
     
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  3. Jan 1, 2007 #2

    marcus

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    As a way of getting an overview of QG directions and progress during the year, I'll list the papers from the quarterly polls. My personal opinion is that Wise paper is the most revolutionary, because it promotes the idea that we ought to get away from flat tangentspace and completely rebuild differential geometry Cartan-style.

    Differential geometry is fundamentally the way humans model spacetime
    it is the workshop where we keep our idea of the CONTINUUM and tinker with it. If you propose that the tangentspace at every point should no longer be a vectorspace, but should embody a "lambda" or cosmo parameter. If you propose that the tangentspace should be the quotient of two Liegroups G/H (which Cartan apparently did and Wise is echoing and ampllifying) then you are screwing around with the idea of the continuum bigtime. Also the Wise paper is very easy to read compared to some others. So I think it is the most fun and revolutionary of all the 2006 QG papers.

    But that is just my personal view of it. So I urge anybody else who follows current background independent QG research to propose what you think is most revolutionary: PLEASE ADD TO THE LIST if you have other B.I. QG favorites. I am going to list, just as a suggestion of the kind of thing you could pick from, what was on our polls.
     
    Last edited: Jan 1, 2007
  4. Jan 1, 2007 #3

    marcus

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    ====first quarter poll====

    Abhay Ashtekar
    http://arxiv.org/abs/gr-qc/0604013
    Quantum Nature of the Big Bang: An Analytical and Numerical Investigation I

    John Baez et al
    http://arxiv.org/abs/gr-qc/0603085
    Exotic Statistics for Loops in 4d BF Theory

    Louis Crane
    http://arxiv.org/abs/gr-qc/0602120
    Categorical Geometry and the Mathematical Foundations of Quantum General Relativity

    Laurent Freidel et al
    http://arxiv.org/abs/gr-qc/0604016
    Hidden Quantum Gravity in 3d Feynman diagrams

    Gerard 't Hooft
    http://arxiv.org/abs/quant-ph/0604008
    The mathematical basis for deterministic quantum mechanics

    Thanu Padmanabhan
    http://arxiv.org/abs/astro-ph/0603114
    Dark Energy: Mystery of the Millennium

    ====second quarter poll====

    1. one by Padmanabhan
    http://arxiv.org/gr-qc/0606061
    Gravity: A New Holographic Perspective
    T. Padmanabhan

    2. two by Rovelli
    http://arxiv.org/gr-qc/0604044
    Graviton propagator in loop quantum gravity
    Eugenio Bianchi, Leonardo Modesto, Carlo Rovelli, Simone Speziale
    http://arxiv.org/quant-ph/0604064
    Relational EPR
    Matteo Smerlak, Carlo Rovelli

    3. two by Ashtekar
    http://arxiv.org/gr-qc/0605011
    Gravity, Geometry and the Quantum
    Abhay Ashtekar
    http://arxiv.org/gr-qc/0602086
    Quantum Nature of the Big Bang
    Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh

    4. two by Baez
    http://arxiv.org/abs/gr-qc/0605087
    Quantization of strings and branes coupled to BF theory
    John C. Baez, Alejandro Perez
    http://arxiv.org/abs/math.DG/0511710
    Higher Gauge Theory
    John C. Baez, Urs Schreiber

    5. three by Majid
    http://arxiv.org/hep-th/0604132
    Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry
    Shahn Majid
    http://arxiv.org/hep-th/0604130
    Algebraic approach to quantum gravity II: noncommutative spacetime
    Shahn Majid
    http://arxiv.org/hep-th/0601004
    Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
    L. Freidel, S. Majid

    ====third quarter poll====

    http://arxiv.org/abs/hep-th/0608221
    A Lorentzian version of the non-commutative geometry of the standard model of particle physics
    John Barrett

    http://arxiv.org/abs/hep-th/0608226
    Noncommutative Geometry and the standard model with neutrino mixing
    Alain Connes

    http://arxiv.org/abs/gr-qc/0607014
    Particles as Wilson lines of gravitational field
    Laurent Freidel, Jerzy Kowalski-Glikman, Artem Starodubtsev

    http://arxiv.org/abs/quant-ph/0608243
    Relational physics with real rods and clocks and the measurement problem of quantum mechanics
    Rodolfo Gambini, Jorge Pullin

    http://arxiv.org/abs/quant-ph/0609109
    Could quantum mechanics be an approximation to another theory?
    Lee Smolin

    ====fourth quarter poll====

    http://arxiv.org/abs/hep-th/0610241
    Gravity and the standard model with neutrino mixing
    Ali H. Chamseddine, Alain Connes, Matilde Marcolli

    http://arxiv.org/abs/hep-th/0611042
    Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
    Aristide Baratin, Laurent Freidel

    http://arxiv.org/abs/gr-qc/0611154
    MacDowell-Mansouri gravity and Cartan geometry
    Derek K. Wise

    http://arxiv.org/abs/gr-qc/0612071
    Plebanski Theory and Covariant Canonical Formulation
    Sergei Alexandrov, Eric Buffenoir, Philippe Roche

    http://arxiv.org/abs/hep-th/0612170
    From noncommutative kappa-Minkowski to Minkowski space-time
    Laurent Freidel, Jerzy Kowalski-Glikman, Sebastian Nowak
     
    Last edited: Jan 1, 2007
  5. Jan 1, 2007 #4
    Hi Marcus,

    This list is a great snapshot on research directions in quantum gravity this year. Thanks for providing it.

    Happy 2007.

    Christine
     
  6. Jan 1, 2007 #5

    marcus

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    Happy 2007 to you too, Christine!

    You are the adept of that skill (delineating QG and making directions visible). The righthand margin of your blog always had the seeds of an overall QG survey-with-highlights. That blog made a real contribution.


    Here I am not sure we have an adequate snapshot quite yet :smile:. What I am asking for is other people's ideas, and other people's picks of significant research to watch.

    this list AFAIK is just what somehow accumulated thru the operation of no great wisdom. But yeah! maybe it does serve as a reminder of some of the active research directions today. Thanks.
     
    Last edited: Jan 1, 2007
  7. Jan 1, 2007 #6
    Hi Marcus,

    I think you are an excellent observer on what is currently going on in quantum gravity research, but not only that. You are able to understand -- at a level good enough to see the "grand scheme of things" in the various subfields -- and analyse the trends, impacts, trace the various collaborations involving the young and experienced researchers alike. And you also spend a good deal of time actually studying some of these investigations in a deep level.

    Quantum gravity is exceedingly fascinating to me.

    Best wishes
    Christine
     
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