Does projective geometry have any role in theoretical physics?
To be honest, I’m not really sure what projective geometry is and how it’s different from topology. Take a manifold without a metric or local affine geometry and all you have is a topology. Geometry isn’t introduced until we define a metric or affine connection. According to wiki, projective geometry is the geometric leftovers of a geometric space minus a metric and affine connection…which is just a topological space. So I’m confused. Anyway, I’m sure mathematical physicists use it, but I’ve studied everything from classical mechanics, to quantum mechanics, to bosonic string theory, to E&M, to general classical field theories, to quantum field theory, etc and simply haven’t seen ‘projective geometries’ used. Edit: Note, mathematical physics and theoretical physics are not the same thing. Mathematical physicists prove the mathematical consistency of things theoretical physicists thought of and experimental physicists confirmed empirically 60 years ago using analysis, number theory, to
