Four-dimensional quantum field theory
Yang–Mills existence and the mass gap.
A constructive proof for pure Yang–Mills theory on ℝ⁴, from the Wilson lattice law to a nontrivial Wightman quantum field theory.
Unconditional proof claimed in Volumes I–III. Independent expert review ongoing.
Developed primarily with GPT‑5 under human research direction. How the collaboration worked →
spec(H) = {0} ∪ [Δ, ∞)
A mathematical foundation for one of physics’ central theories.
Yang–Mills theory describes the gauge fields behind the strong and weak nuclear forces. Physicists use it with extraordinary success, yet in four dimensions its mathematical existence—and the origin of its positive mass scale—has resisted proof.
The paper presents a constructive solution: begin with a precise finite lattice theory, control its behaviour across scales, take the continuum limit, and reconstruct the corresponding quantum field theory.
The central claim
For every compact connected non-abelian gauge group with simple Lie algebra, the construction yields a nontrivial pure Yang–Mills Wightman theory on ℝ⁴ with a unique vacuum and a strictly positive Hamiltonian mass gap.Read the precise statement
How it was developed
A proof built through human–AI collaboration.
GPT‑5 carried much of the exploratory mathematics, drafting, proof assembly, source tracing, and adversarial revision. Leslie P. Polzer directed the research, chose the programme, judged the outputs, and takes responsibility for the claim.
The AI is part of the provenance—not evidence that the theorem is true. The evidence is the proof, and the proof must survive expert scrutiny.
AI methodology and disclosureExplore the work
Start broad. Go deeper when you want to.
The proof, canonical volumes, and physics application now live on separate pages. The introduction stays an introduction.
Open call
Help test the proof.
The project is seeking specialists in constructive quantum field theory, rigorous renormalisation, Osterwalder–Schrader reconstruction, operator theory, and lattice gauge theory for full or modular review.
Review the proof