A simple conceptual question today: is it true that QFT can only be approached in a non-perturbative way only through the functional methods (like 1/N), while in the Hamiltonian formalism we can only do the perturbation theory?
In QM, the functional methods are, of course, widely-known for finding the non-perturbative corrections 1. However, there also exist certain methods based on the Hamiltonian formalism. For example, studying the resolvent operator of the Schrodinger equation 2. Alternatively, one can employ the Uniform WKB quantisation condition 3.
I know that in QFT people also construct the trans-series expansions. But what methods do they use?..