General Spinor Structures on Quantum Spaces

Details General Spinor Structures on Quantum Spaces General Spinor Structures on Quantum Spaces

2000-04-24

arxiv.org/abs/math/0004143v1

Mathematics

Quantum Algebra

40 pages, AMSLaTeX; Visit http://www.matem.unam.mx/~micho for the latest versions of this and related author's papers

Scientific paper

A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford and spinor bundles, a Hodge *-operator, appropriate integration operators, and mutual relations of these objects. We also present a self-contained formalism of braided Clifford algebras. Quantum phenomena appearing in the theory are discussed, including a very interesting example of the Dirac operator associated to a quantum Hopf fibration.

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