Exact computation for interacting quantum field theories

Develop exact, non-perturbative methods to compute transition amplitudes and correlation functions via path integrals for interacting quantum field theories whose Lagrangians include interaction terms beyond quadratic, thereby avoiding reliance on perturbative expansions.

Background

The paper explains that predictions in quantum field theory are ideally obtained from path integrals for transition amplitudes or correlation functions. While exact calculations are available for theories with at most quadratic Lagrangians (non-interacting cases), interacting field theories lack exact solution methods, necessitating perturbative expansions.

This gap motivates reliance on Feynman-diagrammatic perturbation theory and renormalization, but it explicitly highlights a core technical limitation: the absence of exact calculation techniques for interacting QFTs. Addressing this limitation would be fundamental for improving precision and scope beyond perturbation theory.