Schild's Ladder Parallel Transport Procedure for an Arbitrary Connection |
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| Authors: | Arkady Kheyfets Warner A. Miller Gregory A. Newton |
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| Affiliation: | (1) Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695-8205;(2) Theoretical Astrophysics Group (T-6 MS B288), Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545;(3) Department of Physics, North Carolina State University, Raleigh, North Carolina, 27695-8208 |
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| Abstract: | We analyze the Schild's ladder parallel transport procedure for an arbitraryconnection. We demonstrate that the procedure, while it can be performed forany connection, in fact is only capable of detecting the symmetric part of thisconnection. In geometries with a symmetric connection it fulfills its goal toexpress connection and parallel transport of any vector in terms of geodesics ofsuch geometries. |
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