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Schild's Ladder Parallel Transport Procedure for an Arbitrary Connection

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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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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695-8205

    Arkady Kheyfets

  2. Theoretical Astrophysics Group (T-6 MS B288), Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545

    Warner A. Miller

  3. Department of Physics, North Carolina State University, Raleigh, North Carolina, 27695-8208

    Gregory A. Newton

Authors
  1. Arkady Kheyfets
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  2. Warner A. Miller
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  3. Gregory A. Newton
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Kheyfets, A., Miller, W.A. & Newton, G.A. Schild's Ladder Parallel Transport Procedure for an Arbitrary Connection. International Journal of Theoretical Physics 39, 2891–2898 (2000). https://doi.org/10.1023/A:1026473418439

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  • DOI: https://doi.org/10.1023/A:1026473418439

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