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Gauge transformations on locally trivial quantum principal fibre bundles

Dirk Calow·Rainer Matthes
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Abstract

If P, B, H are the algebras of the total space, the base space, and the structure group of a locally trivial principal fibre bundle (QPFB), left (right) gauge transformations are defined as automorphisms of the left (right) B-module P which are adapted to the coaction of the Hopf algebra H and to the covering related to the local trivializations. Covariant derivatives on a QPFB are always transformed into covariant derivatives. This is true for connections only for special choices of the differential structure on H and/or if one restricts to algebra automorphisms. There are analogues of the classical formulas relating local connection forms and their gauge transforms.

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Dirk Calow, Rainer Matthes. 2000-02-27. Gauge transformations on locally trivial quantum principal fibre bundles. https://arxiv.org/abs/math/0002230

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