Choice in General Relativity: Metric, . Directly determines

Riemannian geometry; Geometrodynamics.

In all other interactions, by contrast, the basic variable is a Connection, i.e., a matrix valued vector potential .

Gauge theories: Connection-dynamics

Connections: Vehicles for parallel transport.

Classical singularities are gates to Physics Beyond Einstein.

— Introduction to Loop Quantum Gravity

— Abhay Ashtekar

2011.06.17 Friday ACHK