Geometric Charge
Geometric Charge (IV.D58) is the τ-categorical generalization of charge: the winding-number / topological holonomy invariant of a defect bundle on any closed fiber loop. Specializations recover electric charge (IV.D84), color charge (IV.D154), and the total topological charge (IV.D214).
τ-Definition
Geometric Charge (IV.D58) is the τ-categorical generalization of charge: the winding-number / topological holonomy invariant of a defect bundle on any closed fiber loop. Specializations recover electric charge (IV.D84), color charge (IV.D154), and the total topological charge (IV.D214).
Categorical invariant. GeometricCharge(B, ℓ) := winding number of B's holonomy on the closed loop ℓ ⊂ T²; an E1 topological invariant that subsumes all sector-specific charges.
Primary registry anchor:
IV.D58
τ-Derivation Chain
-
I.K0— Universe Postulate establishes τ -
IV.D11— Physical Quantity Template establishes dimensional/topological invariants -
IV.D58— Geometric Charge = winding-number invariant on closed fiber loops -
IV.D84— Electric Charge specializes Q_geom to the U(1)/EM sub-fiber -
IV.D154— Color Charge specializes Q_geom to the SU(3)/strong sub-fiber -
IV.D214— Total topological charge sums the sector-specific specializations
Lean modules referenced:
TauLib.BookIV.Sectors.CouplingFormulas
SI Translation
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- Q_geom is dimensionless — calibration enters only via sector-specific specializations
Manuscript reference: manuscript-sources/book-04/part03-charge-template/ch-geometric-charge.tex