GoKawiilPhysicist John Baez ties three particle generations to E7 exceptional algebra
Mathematical physicist John Baez has published a new paper arguing that the puzzling existence of exactly three generations of quarks and leptons may emerge naturally from the exceptional Lie group E7, building on earlier work linking the Standard Model's gauge group to the exceptional Jordan algebra. The paper is his third in a series exploring whether unusual mathematical structures built from the octonions can explain quirky features of particle physics rather than treating them as accidental.
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Physicists have had no accepted explanation for why nature repeats its fundamental particles in three near-identical copies, and progress on new fundamental theories has stalled since the early 1980s. Finding a mathematical structure that makes this pattern seem inevitable rather than arbitrary would be a significant conceptual advance, even without new experimental predictions, because it could hint at deeper principles underlying the Standard Model.
- Baez's new paper links the three generations of quarks and leptons to the exceptional Lie group E7.
- It follows prior work connecting the Standard Model's gauge group to the exceptional Jordan algebra, done with Michel Dubois-Violette, Ivan Todorov and Paul Schwahn.
- The research is speculative but aims to find a natural mathematical reason for a long-unexplained feature of particle physics.
On Quaternions and Octonions (Conway & Smith) — If this dive into exceptional algebraic structures and octonions piqued your curiosity, Conway and Smith's classic is the natural next step. It builds up quaternions and octonions from geometry and symmetry, giving you the background needed to appreciate why E7 and the exceptional groups keep tempting physicists.
See On Quaternions and Octonions (Conway & Smith) on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.Source: johncarlosbaez.wordpress.com, 2026-08-24
Published there as: “Three Generations in E7”
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