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.

References

For interacting field theories (i.e. all theories representing fields that occur in our actual world) we don’t know how to do this calculation exactly, so instead we typically make predictions using a perturbative expansion, in which we expand around the more easily calculated free theory.

— Quantum Field Theory and the Limits of Reductionism  (2407.20457 - Adlam, 2024) in Section 2, Background

It could be interesting to more thoroughly investigate whether the analytical structure of the exact two-point function explored here is amenable to study via these methods, but we leave this for future work.

— Deep neural networks as lattice gauge theories  (2608.19331 - Jefferson et al., 19 Aug 2026) in Appendix B, subsection “Not-quite-full computation”