Fiber Bundles of the Complex Projective Space and Their Relation to Quantum Physics

Abstract

The complex projective space CPn is the space of lines through the origin in Cn+1 with an equivalence relation defined by Z ~ λZ\u27 for λ ∈ C*. We define the points under the equivalence relation as homogeneous coordinates, represented by [Z0 : Z1 : ... Zn]. Since all Z,sub\u3ei cannot equal zero, we can find a unique set of n coordinates (z1,...,zn) such that [Z0 : Z1 : ... : Zn] ~ [1 : z1 : ... : zn] where zi = Zi\Z0