Can we make a connection? Consider the phase space of a point particle in R^3. Six numbers are required, three for position and three for velocity. Now consider an isotropic vector, X, in C^3 with X*X = 0. X = (x1,x2,x3), X*X = (x1*x1 + x2*x2 + x3*x3), x1 = c1 + i*c2, x1*x1 = (c1*c1 + c2*c2 +2*i*c1*c2) From: http://www.sjsu.edu/faculty/watkins/spinor.htm "It can be shown that the set of isotropic vectors in C^3 form a two dimensional surface. This two dimensional surface can be parametrized by two coordinates, z0 and z1 where z0 = [(x1-ix2)/2]1/2 z1 = i[(x1+ix2)/2]1/2. The complex two dimensional vector Z=(z0, z1) Cartan calls a spinor. But a spinor is not just a two dimensional complex vector; it is a representation of an isotropic three dimensional complex vector." Let the real part of X represent the position of a point particle and let the imaginary part of X represent the velocity of the same particle. If we require X*X = 0 how does that restrict the phase space path of a particle? Thank you for any help.