Quantum Gravity via Manifold Positivity

  • Michael H. Freedman


The macroscopic dimensions of space-time should not be input but rather output of a general model for physics. Here, dimensionality arises from a recently discovered mathematical bifurcation: “positive versus indefinite manifold pairings.” It is used to build actions on a “formal chain” of combinatorial space-times of arbitrary dimension. The context for such actions is 2-field theory where Feynman integrals are not over classical, but previously quantized configurations. A topologically enforced singularity of the action can terminate the dimension at four and, in fact, the final fourth dimension is Lorentzian due to light-like vectors in the four dimensional manifold pairing. Our starting point is the action of “causal dynamical triangulations” but in a dimension-agnostic setting. Curiously, some hint of extra compact dimensions emerges from our action.


Hilbert Space Quantum Gravity Kinetic Term Formal Chain Wick Rotation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Microsoft CorporationUniversity of CaliforniaOaklandUSA

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