Affine Space of Connections and Why the Gauge Group Must Be Inhomogeneous
Connections don't form a vector space, and that single fact quietly forces a bigger symmetry.
The Inhomogeneous Group G: Actions and "Transport"
Once you admit translations in connection space, you're forced into a semidirect product — and it acts on connections in one line.
The Distinguished Background
Choosing an affine origin (without adding structure) so transport becomes well-defined.
Augmented Torsion
The transport displacement that actually transforms like a field.
Gauge-Covariant Bookkeeping: Double Disease Cancellation
Two bad transformation laws, one good variable.