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Phase space

  1. May 5, 2009 #1
    1. The problem statement, all variables and given/known data

    Trying to derive a bundle map for a tangent space on a sphere. This is in line with some online courses in QM and phase space topology. I'm not doing an assignment as such (I'm a postgrad though).
    This is also in line with keeping up with tensor calculus (and the symmetry of space+time), since QM is way easier in that case.


    2. Relevant equations

    a is a 2 deg vertex [tex] a(\phi_i \bar \phi_j) [/tex]. i,j are state indices; i indexes a null-vertex in the graph G(V,E), the vertex is aligned as a line (a geodesic) on the sphere, w/ edges at +/- infinity.
    [tex] \phi_i [/tex] recovers [tex] \bar \phi_j [/tex] at a, the crossing in G.
    a = (p + ic) where c is the color at the crossing indexed by j.

    This is the trivial fiber over the base space S' and G: G -> B needs a continuous sectional function which is smooth over E the inner measure, M the manifold (sphere), F the fiber space and B the base space or map.



    3. The attempt at a solution

    Write a bivector form for the vertices/crossings and derive the section and projective functions that way?

    ed: s'ok, I think I just realised it's a matter of a swapping for vertex-edge pairs from one to the other space, and so on...(doh!)
     
    Last edited: May 5, 2009
  2. jcsd
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