Renormalizable Gravitational Action That Reduces to General Relativity on the Mass-Shell

Abstract

We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement. Implications of this equation are discussed in the paper. In particular, we show (in the last section) that this equation is the transformation that relates four-dimensional physics to two-dimensional physics.

Keywords

• scalar curvature
• renormalizability