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Quantum Gravity via Manifold Positivity

In: Essays in Mathematics and its Applications

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  • Michael H. Freedman

    (University of California, Microsoft Corporation)

Abstract

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.

Suggested Citation

  • Michael H. Freedman, 2012. "Quantum Gravity via Manifold Positivity," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Essays in Mathematics and its Applications, edition 127, pages 111-140, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28821-0_6
    DOI: 10.1007/978-3-642-28821-0_6
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