A SO(1,3) gauge theory of quantum gravity: quantization and renormalizability proof

Abstract

Abstract A new SO(1,3) gauge field theory classically equivalent to general relativity in a limiting case is quantized and the gauge-fixed path integral representation of the quantum effective action (QEA) is derived. Both the gauge-fixed classical action and the QEA are shown to be invariant under nilpotent BRST variations of the gauge, matter, ghost, antighost and Nakanishi–Lautrup fields defining the theory and a Zinn-Justin equation constraining the QEA is derived. Dimensional analysis and the various linear constraints put on the QEA plus the ones from the non-linear Zinn-Justin equation are deployed to demonstrate full renormalizability such that all infinities appearing in a perturbative expansion of the QEA can be absorbed into the gauge-fixed classical action solely by field renormalizations and coupling redefinitions—providing the third step in consistently quantizing the SO(1,3) gauge field theory at hands, and with it potentially gravity.