Quantum Groups on Fibre Bundles

Details Quantum Groups on Fibre Bundles Quantum Groups on Fibre Bundles

1994-01-19

arxiv.org/abs/hep-th/9401085v1

Commun.Math.Phys.166:279-316,1994

Physics

High Energy Physics

High Energy Physics - Theory

50 pages

Scientific paper

10.1007/BF02112317

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of principal fibre bundles like associated bundles and differential calculi are carried over to the quantum case. At the end $q$-deformed instanton models are introduced for every integral index.

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