Quantum Gravity via Manifold Positivity

Michael H. Freedman ()
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Michael H. Freedman: University of California, Microsoft Corporation

A chapter in Essays in Mathematics and its Applications, 2012, pp 111-140 from Springer

Abstract: 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.

Keywords: Hilbert Space; Quantum Gravity; Kinetic Term; Formal Chain; Wick Rotation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-28821-0_6

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DOI: 10.1007/978-3-642-28821-0_6

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