2019/06/29 by Roberto Zucchini, Zucchini, Roberto
Physics and Astronomy · #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.1907.00155
The geometry of the total space of a principal bundle with regard to the\naction of the bundle's structure group is elegantly described by the bundle's\noperation, a collection of derivations consisting of the de Rham differential\nand the contraction and Lie derivatives of all vertical vector fields and\nsatisfying the six Cartan relations. Connections and gauge transformations are\ndefined by the way they behave under the action of the operation's derivations.\nIn the first paper of a series of two extending the ordinary theory, we\nconstructed an operational total space theory of strict principal 2--bundles\nwith reference to the action of the structure strict 2--group. Expressing this\nlatter through a crossed module ( mathsansE, mathsansG), the operation is\nbased on the derived Lie group mathfrake[1] rtimes mathsansG. In this\npaper, the second of the series, an original formulation of the theory of\n2--connections and 1-- and 2--gauge transformations of principal\n2--bundles based on the operational framework is provided.\n