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On non-Abelian holonomies. (English) Zbl 1043.83015

Summary: We provide a method and results for the calculation of the holonomy of a Yang-Mills connection in an arbitrary triangular path, in an expansion (developed here to fifth order) in powers of the corresponding segments. The results might have applications in generalizing to Yang-Mills fields previous calculations of the corrections to particle dynamics induced by loop quantum gravity, as well as in the field of random lattices.

MSC:

83C45 Quantization of the gravitational field
53C29 Issues of holonomy in differential geometry
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