Non-perturbative  foundational problems of QFT and, in particular, of gauge theories:  problems and results are discussed in my book "An introduction to non-perturbative foundations of quantum field theory, Oxford Univ. Press 2013. In collaboration with Giovanni Morchio, I am interested in the non-perturbative control of the infrared problem in QED and in the derivation of an LSZ formulation for the S-matrix. Another research interest is the link between gauge invariance of the ground state and the non-regular (polymer) Weyl quantization, with applications to many body theory and loop  quantum gravity.