Joseph Conlon

John Preskill Verified account @preskill · 4d

Wise words from @JosephPConlon (and from Steve Weinberg): "Go for the messes - that's where the action is."

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Dan Roberts Verified account @danintheory · Oct 26

The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.

As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean.

Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials.

Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory.

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