Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras

Details Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras

2003-10-03

arxiv.org/abs/hep-th/0310026v4

Int.J.Mod.Phys. A19 (2004) 3395-3408

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 13 pages, v3: minor additions, added references, v4: corrected typos, to appear in IJMPA

Scientific paper

10.1142/S0217751X04019810

Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling spacetimes by non-commutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model processes where one fuzzy space splits into several fuzzy spaces. For example we can discuss the quantum transition where the fuzzy sphere for angular momentum J splits into fuzzy spheres for angular momenta K and L.

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