13.  Gauge Structure, Quantisation, and the Standard Model

The known particles are sorted by three symmetries, written SU(3), SU(2) and U(1). Nobody knows why those three and not some others. This chapter argues they were never a choice: they are symmetries the substrate already had, read off after the projection.

• 13.1. From U(1) to the full Standard Model gauge group
• 13.2. Path-integral quantisation of the projected theory
• 13.3. Local gauge symmetry: the photon as a connection
• 13.4. SU(2)L from threshold topology: the electroweak doublet
• 13.5. Colour SU(3)c: octonionic origin and Casimir decomposition
• 13.6. Consistency of the octonionic interpretation
• 13.7. The internal algebra AF derived from P1–P3
• 13.8. Gauge anomaly cancellation as a structural check
• 13.9. U(1)Y hypercharges compatible with PST structure
• 13.10. The Standard Model Lagrangian as leading-order projection
• 13.11. Summary