For this problem you will use the parallel propagator introduced in Appendix I to see how the Riemann tensor arises from parallel transport around an infinitesimal loop. Consider the following loop: Using the inftnite series expression for the parallel propagator, compute to lowest nontrivial order in δa and 8 b the transformation induced on a vector that is parallel transported around this loop from A to B to C to D and back to A, and show it is proportional to the appropriate components of the
For this problem you will use the parallel propagator introduced in App…
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