Geodesic
Gauge invariant surface holonomy and monopoles
Theory and applications of categories, Tome 30 (2015), pp. 1319-1428

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There are few known computable examples of non-abelian surface holonomy. In this paper, we give several examples whose structure 2-groups are covering 2-groups and show that the surface holonomies can be computed via a simple formula in terms of paths of 1-dimensional holonomies inspired by earlier work of Chan Hong-Mo and Tsou Sheung Tsun on magnetic monopoles. As a consequence of our work and that of Schreiber and Waldorf, this formula gives a rigorous meaning to non-abelian magnetic flux for magnetic monopoles. In the process, we discuss gauge covariance of surface holonomies for spheres for any 2-group, therefore generalizing the notion of the reduced group introduced by Schreiber and Waldorf. Using these ideas, we also prove that magnetic monopoles form an abelian group.

Publié le :
Classification : Primary 53C29, Secondary 70S15
Keywords: Surface holonomy, gauge theory, 2-groups, crossed modules, higher-dimensional algebra, monopoles, gauge-invariance, non-abelian 2-bundles, iterated integrals 
@article{TAC_2015_30_a41,
     author = {Arthur J. Parzygnat},
     title = {Gauge invariant surface holonomy and monopoles},
     journal = {Theory and applications of categories},
     pages = {1319--1428},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a41/}
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Arthur J. Parzygnat. Gauge invariant surface holonomy and monopoles. Theory and applications of categories, Tome 30 (2015), pp. 1319-1428. http://geodesic.mathdoc.fr/item/TAC_2015_30_a41/