Applications of the Fundamental Theorems of Projective and Affine Geometry in Physics

The closely related fundamental theorems of projective and affine geometry are keys to understanding some important but seemingly unrelated topics in mathematical physics. Specifically, they can be used in proofs of Wigner's theorem on ray correspondences in quantum mechanics and also to establish the scale extended Poincare group as the basic causality preserving symmetry group of special relativity. We describe these two theorems and show their roles in establishing the just mentioned results.