TOWARDS A THEORY OF SPACETIME STRUCTURE AT VERY SHORT DISTANCES

Renormalization-group arguments are summarized which suggest that at distances shorter than the Planck length the spacetime geometry should be asymptotically scale invariant. A new locally scale-invariant extension of general relativity is then proposed based on Weyl's conformally invariant geometry. It is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances. Finally, the theory incorporates the non-linear sigma model, which suggests a new approach to the calculation of non-perturbative, short-distance effects in quantum gravity. © 1979.