Affine Fields and Signature Geometry

This monograph develops a unified geometric interpretation of classical and quantum physics based on the principle of representational compatibility. Building on the affine quantization program formulated in the work of Riccardo Fantoni, we reinterpret quantization not as a fixed algebraic prescription but as a geometry-dependent transformation between representational regimes. Classical mechanics, canonical quantization, and affine quantization are shown to correspond to distinct charts in a generalized signature space, where admissibility, boundarystructure, and global closure determine the stability of representation.