Geometric Approach to Quantum Theory. L-functionals

This publication consists of slides from my talk at the Simons Center for Geometry and Physics in 2024. It contains a brief review of the L-functional formalism, along with a discussion of its possible applications to QED, linearized gravity, and quenched disorder. The most interesting part is the discussion of the infrared problem in QED and a conjecture on how to construct an infrared-finite perturbation theory for QED.