Covariant derivative on non-linear fiber bundles |
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Authors: | Pavel Krtou? |
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Institution: | (1) Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Praha 8, Czech Republic |
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Abstract: | A gauge field is usually described as a connection on a principal bundle. It induces a covariant derivative on associated
vector bundles, sections of which represent matter fields. In general, however, it is not possible to define a covariant derivative
on non-linear fiber bundles, i.e. on those which are not vector bundles. We definelogarithmic covariant derivatives acting on two special non-linear fiber bundles — on the principal bundle and on the local gauge group bundle. The logarithmic
derivatives map from sections of these bundles to the sections of the local gauge algebra bundle. Some properties of the logarithmic
derivatives are formulated. |
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Keywords: | PACS" target="_blank">PACS 02 40 Hw 11 15 -q 03 50 Kk |
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