Gauge Theories as Distributions of Affine Defects

Geometric gauge theory provides a mathematical foundation for the most successful innovations in twentieth-century theoretical physics. The theories use symmetry groups, connections on fiber bundles, and concepts of parallel translation and curvature to model basic physics. More specifically, spacetime translations and projective conformal transformations model linear momentum; affine torsion, including torsion trace, models intrinsic angular momentum; conformal dilations model quantum wave mechanics; and unitary symmetry models elementary particles. The present work combines these basic gauge symmetries in a common framework as distributions of discrete defects in affine spaces, where each type of gauge field can be interpreted geometrically as a distribution of discrete defects in a regular lattice. The final section suggests in general terms research programs to search for distributions of discrete defects in regular lattices that underlie gauge theories.