Background independence in gauge theories
- Mojtaba Taslimitehrani (Max Planck Institute for Mathematics in the Sciences, Germany)
Abstract
Classical field theory is background independent in the sense that it is insensitive to the split of the field into a background configuration and a dynamical perturbation. At the quantum level, we define background independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A QFT is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and show that all potential obstructions can be removed by finite renormalization. We also comment on the background-independence of perturbative quantum gravity. Joint work with Jochen Zahn. Based on arXiv:1804.07640.