What Are the Differences Between Riemannian and Lorentzian Spin Networks?

[meteor]

Can someone tell me what's the difference between a Riemannian spin network and a Lorentzian spin network?

 

[selfAdjoint]

It's the underlying manifold they are implemented on. Although spin networks look forward to replacing metric geometry, they must as yet be built on an underlying manifold. That manifold can be either Riemannian, with a Euclidean tangent space, or Lorentzian, with a Minkowskian tangent space. The spacetime of GR is Lorentzian.

Generally speaking a Lorentzian network is harder to work with because you have to deal with links in timelike directions. For this reason you will see basic work on networks being carried out in a spacelike slice - a three dimensional Riemannian manifold embedded in the higher dimensional Lorentzian one.