Renormalizing Spacetime

TL;DR

This paper introduces a Weyl transformation approach to gravity's field renormalization, making length, time, energy, and momentum scale-dependent, and applies it to quantum gravity issues like non-conformal scaling and non-renormalizability.

Contribution

It proposes a specific Weyl transformation for gravity's renormalization, linking scale dependence of physical quantities to a minimum resolvable distance.

Findings

Derived a functional form for the field renormalization factor.

Applied the transformation to quantum gravity problems.

Provided insights into non-conformal scaling and non-renormalizability.

Abstract

We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate the functional form of the field renormalization factor by imposing a minimum resolvable distance scale under an infinitesimal Weyl transformation. The derived transformation is applied to two key problems in quantum gravity, its non-conformal scaling, and non-renormalizability.