Riemann sphere
The Riemann sphere has many uses in physics. In quantum mechanics, points on the complex projective line are natural values for photon polarization states, spin states of massive particles of spin , and 2-state particles in general (see also Quantum bit and Bloch sphere). The Riemann sphere has been suggested as a relativistic model for the celestial sphere. In string theory, the worldsheets of strings are Riemann surfaces, and the Riemann sphere, being the simplest Riemann surface, plays a significant role. It is also important in twistor theory.