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Algebraic QFT and Quantum Gravity

  1. Oct 25, 2006 #1


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    Kea posted this on another thread:

    The Tomita-Takesaki results are and exciting breakthrough in AQFT, by now getting to be pretty well understood. The beginnings of it are in Haag's book Local Quantum Physics.

    Another line of work in AQFT that approaches the idea of matter in QG is represented by the work of Klaus Fredenhagen and his colleagues. A recent example is gr-qc/0603079, Towards a Background Independent Formulation of Perturbative Quantum Gravity, by Romeo Brunetti and Klaus Fredenhagen.
    A brief quotation will give the flavor.

    Last edited: Oct 25, 2006
  2. jcsd
  3. Oct 25, 2006 #2


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    Hi selfAdjoint

    Naturally I'm more a fan of the Higher Category approach, but the impression I got yesterday is that the emerging dictionary between Kontsevich, operads etc. on the one hand, and NCG (or AQFT) on the other is beginning to look substantial. That doesn't make me enthusiastic to go away and learn Tomita-Takesaki. On the contrary: it only makes me more convinced that the right way to tell phenomenologists and experimentalists how to calculate stuff is the easier way...with operads. Now on that side, admittedly, the geometry of manifolds is not yet so clear. But we deliberately set out from a different starting point, for physical reasons. Connes and Marcolli want the Riemann hypothesis. We just care about Yang-Mills and mass generation.

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