Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

3D phase space of point particle and spinors.

  1. Jun 18, 2009 #1
    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)



    "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.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: 3D phase space of point particle and spinors.
  1. Space and particles (Replies: 11)