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Feb8-09, 03:00 AM
Hi everyone -- I have a question about the relation between the spin connection and the Christoffel connection.
The spin connection comes from the local (gauge) Lorentz symmetry of how we orient vielbeins at each point in space, it contains a manifold index and two tangent space indices. The Christoffel connection comes from the (also local/gauge) diffeomorphism invariance of general relativity, carrying three manifold indices.
My question is how are these two connections related, or are they both independent degrees of freedom?
See for example Chamseddine hep-th/0511074 (2005) and the discussion in "Beyond the standard model" page 2, Martin Kober ...