Quantum gravity via manifold positivity

Michael H. Freedman

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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.

Original languageEnglish
Title of host publicationEssays in Mathematics and its Applications
Subtitle of host publicationIn Honor of Stephen Smale's 80th Birthday
PublisherSpringer-Verlag Berlin Heidelberg
Pages111-140
Number of pages30
Volume9783642288210
ISBN (Electronic)9783642288210
ISBN (Print)3642288200, 9783642288203
DOIs
StatePublished - 1 Jun 2012
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2012 Springer-Verlag Berlin Heidelberg. All rights are reserved.

ASJC Scopus subject areas

  • General Mathematics

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