Open AccessA SO(1,3) gauge theory of quantum gravity: quantization and renormalizability proof
Author(s) -
C. Wiesendanger
Publication year - 2020
Publication title -
classical and quantum gravity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.528
H-Index - 189
eISSN - 1361-6382
pISSN - 0264-9381
DOI - 10.1088/1361-6382/aba80b
Subject(s) - brst quantization , physics , mathematical physics , quantization (signal processing) , gauge fixing , introduction to gauge theory , path integral formulation , gauge theory , faddeev–popov ghost , quantum gauge theory , supersymmetric gauge theory , nilpotent , theoretical physics , quantum mechanics , quantum , gauge boson , mathematics , pure mathematics , algorithm
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.