Topology change for fuzzy physics: Fuzzy spaces as Hopf algebras

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BALACHANDRAN A., Kurkcuoglu S.

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, vol.19, no.20, pp.3395-3407, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 20
  • Publication Date: 2004
  • Doi Number: 10.1142/s0217751x04019810
  • Journal Name: INTERNATIONAL JOURNAL OF MODERN PHYSICS A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3395-3407
  • Keywords: fuzzy spaces, Hopf algebras, quantum symmetries, MANIFOLDS
  • Middle East Technical University Affiliated: No

Abstract

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 space-times by noncommutative 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.