Small-scale structure of spacetime as the origin of the gravitational constant

Paul K. Townsend
Phys. Rev. D 15, 2795 – Published 15 May 1977
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Abstract

We suggest a means of incorporating the Planck length as a fundamental constant determined by the structure of spacetime. In this scheme the spacetime symmetry group is taken as the de Sitter group with radius of curvature proportional to the Planck length, but we argue that the effects of this curvature are not apparent at elementary-particle length scales. To make the connection with gravity we present a formulation of the gravitational interaction as the gauge theory of the de Sitter group. We obtain an action containing the Einstein-Cartan action, but in which the dimensional gravitational constant G appears naturally as the consequence of the commutation relation of the de Sitter group. We also find a cosmological term, higherderivative couplings of the gravitational field, and a propagating torsion field, which we discuss.

  • Received 1 November 1976

DOI:https://doi.org/10.1103/PhysRevD.15.2795

©1977 American Physical Society

Authors & Affiliations

Paul K. Townsend

  • Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794

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Issue

Vol. 15, Iss. 10 — 15 May 1977

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