Home›Open Questions›Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Open QuestionsDoes a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?." Accessed August 30, 2026. https://dev-mathematics.interactiveatlas.org/open-questions-index/yang-mills-existence-and-mass-gap-open-question.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?. Retrieved August 30, 2026, from https://dev-mathematics.interactiveatlas.org/open-questions-index/yang-mills-existence-and-mass-gap-open-questionCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-does-a-nontrivial-quantum-yang-mills-the, author = {Mathematics Atlas}, title = {Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?}, year = {2026}, url = {https://dev-mathematics.interactiveatlas.org/open-questions-index/yang-mills-existence-and-mass-gap-open-question}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionThe mass gap is well established by physics experiment and by computer simulation, but no one has derived it as a mathematical consequence of the quantum Yang-Mills equations themselves, and no fully rigorous construction of a four dimensional quantum Yang-Mills theory yet exists.What would resolve this A rigorous mathematical construction of quantum Yang-Mills theory on four dimensional space for a compact simple gauge group, together with a proof that it has a mass gap greater than zero.OpenMathematical physicsClay Mathematics InstituteCross-Tradition ConnectionsQuestion OnYang-Mills Existence and Mass Gap, Conjectures Well-attested Source Clay Mathematics Institutetier 1SourcesClay Mathematics Institutetier 1Clay Mathematics Institutehttps://www.claymath.org/millennium/yang-mills-the-maths-gap/View the SourceComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year