The Z/nZ Bundle and the Standard Model: Electroweak Symmetry Breaking as Z/2Z Instantiation and a Structured Formal Proposal for Strong Interaction as Z/3Z Extension
Abstract
I propose that the electroweak and strong sectors of the Standard Model are instantiations of a Z/nZ principal bundle structure at n=2 and n=3 respectively. The central mathematical object is a graded real vector space V = V_G ⊕ V_Q equipped with an involutive operator X: V→V satisfying X² = −Id_V. I prove three theorems: (T1) any involutive operator on a graded bundle has a unique invariant direction with zero curvature, identified with the massless photon; (T2) the minimal cyclic group Z/nZ admitting a closed triangular representation with non-trivial holonomy is Z/3Z, giving the structural origin of three color charges; (T3) color confinement follows as a topological theorem from the closure condition of the Z/3Z bundle. Five corollaries are derived without free parameters: photon masslessness, three-generation structure, color confinement, W/Z mass ratio, and absence of magnetic monopoles. The relation to centre symmetry in SU(N) gauge theories, the Atiyah-Singer index theorem, and Connes' noncommutative geometry programme is established.
Fields of Study & Subjects
Noncommutative and Quantum Gravity Theories
Black Holes and Theoretical Physics
Quantum and Classical Electrodynamics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 26 May 2026
- Language
- EN
- Document type
- Preprint