#### marcus

Science Advisor

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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."

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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."

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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."

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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."

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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."