# Phase space

1. May 5, 2009

### deferro

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 $$a(\phi_i \bar \phi_j)$$. 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.
$$\phi_i$$ recovers $$\bar \phi_j$$ 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