Chapter 14: Characters as Quantum Addresses

The lemniscate 𝕃 is where quantum numbers live. Characters—homomorphisms from fundamental groups to U(1)—enumerate the possible quantum states. This is representation theory meeting topology. The ℤ × ℤ character structure on the torus is already quantization—no additional postulates required. Each character is a quantum address: a discrete label that specifies where a state lives in the CR-admissible mode space.