Learning Simplicity and Structure in Quantum Field Theory

Abstract

Computing scattering amplitudes in quantum field theory is central to enable robust tests of the Standard Model and searches for new physics at collider experiments. While the Lagrangian description is remarkably compact, and apparently simple, extracting predictions requires evaluating Feynman diagrams whose complexity grows rapidly with loop order and particle multiplicity, quickly becoming algorithmically challenging. Remarkably, final results often reduce dramatically, suggesting hidden simplicity that conventional computational methods initially obscure. This dissertation explores how a combination of machine learning, data-driven tools and theoretical insights can uncover, leverage, and discover some of this hidden structure. On the machine learning side, we first demonstrate that transformer neural networks can learn to simplify complicated analytic expressions, involving both polylogarithmic expressions and spinor-helicity amplitudes, producing new compact results for multi-particle scattering. We then show how the known analytic structure of Feynman integrals, combined with high-precision numerical evaluation and lattice reduction algorithms, allows for the exact bootstrapping of multi-loop results. Turning to the S-matrix bootstrap, we implement neural networks as amplitude surrogates and train them to satisfy unitarity constraints. This allows us to reconstruct scattering amplitude phases from differential cross-section data, and leads us to discover new phase-ambiguous solutions. Finally, on the theoretical side, we discuss how to unpack some of the hidden structure in Quantum Field Theories and investigate the non-perturbative structure encoded in perturbative expansions. We resolve longstanding subtleties in the collective coordinate method for path integrals, demonstrate that renormalons arise as saddle points of the one-loop effective action via the quantum scale anomaly, and develop a systematic Lefschetz-thimble decomposition framework, allowing us to connect perturbative and non-perturbative physics in theories with instantons and renormalons.