What is the relationship between a metric connection and a gauge field?

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  1. A metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common equivalent formulations of a metric connection include:



    • A connection for which the covariant derivatives of the metric on E vanish.

    • A principal connection on the bundle of orthonormal frames of E.


A special case of a metric connection is the Riemannian connection, of which the Levi-Civita connection is a particularly important special case.



  1. The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection



metric-spaces vector-bundles fiber-bundles




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    1. A metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common equivalent formulations of a metric connection include:



      • A connection for which the covariant derivatives of the metric on E vanish.

      • A principal connection on the bundle of orthonormal frames of E.


    A special case of a metric connection is the Riemannian connection, of which the Levi-Civita connection is a particularly important special case.



    1. The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection



    metric-spaces vector-bundles fiber-bundles




    share|cite|improve this question






















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      up vote
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      1. A metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common equivalent formulations of a metric connection include:



        • A connection for which the covariant derivatives of the metric on E vanish.

        • A principal connection on the bundle of orthonormal frames of E.


      A special case of a metric connection is the Riemannian connection, of which the Levi-Civita connection is a particularly important special case.



      1. The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection



      metric-spaces vector-bundles fiber-bundles




      share|cite|improve this question













      1. A metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any two vectors will remain the same when those vectors are parallel transported along any curve. Other common equivalent formulations of a metric connection include:



        • A connection for which the covariant derivatives of the metric on E vanish.

        • A principal connection on the bundle of orthonormal frames of E.


      A special case of a metric connection is the Riemannian connection, of which the Levi-Civita connection is a particularly important special case.



      1. The "gauge covariant" version of a gauge theory accounts for this effect by introducing a gauge field (in mathematical language, an Ehresmann connection) and formulating all rates of change in terms of the covariant derivative with respect to this connection




      metric-spaces vector-bundles fiber-bundles





      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 9 at 16:20









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