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The field copy problem: to what extent do curvature (gauge field) and its covariant derivatives determine connection (gauge potential)?

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Abstract

We show that a connection of a principal bundle is determined up to (global) gauge equivalence by the curvature and its covariant derivatives provided that the infinitesimal holonomy group is of constant dimension and the base space is simply connected. If the dimension of the infinitesimal holonomy group varies, there may be obstructions of a topological nature to the existence of a global or even local gauge equivalence between two connections whose curvatures and covariant derivatives of curvature agree everywhere. These obstructions are analyzed and illustrated by examples.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 27650, Raleigh, N.C., USA

    Mark A. Mostow

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  1. Mark A. Mostow
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Communicated by A. Jaffe

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Mostow, M.A. The field copy problem: to what extent do curvature (gauge field) and its covariant derivatives determine connection (gauge potential)?. Commun.Math. Phys. 78, 137–150 (1980). https://doi.org/10.1007/BF01941974

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  • DOI: https://doi.org/10.1007/BF01941974

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