Communications in Mathematical Physics

, Volume 259, Issue 3, pp 729–759 | Cite as

The Dirac Operator on SU q (2)

  • Ludwik Dabrowski
  • Giovanni Landi
  • Andrzej Sitarz
  • Walter van Suijlekom
  • Joseph C. Várilly


We construct a 3+-summable spectral triple Open image in new window over the quantum group SU q (2) which is equivariant with respect to a left and a right action of Open image in new window The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ludwik Dabrowski
    • 1
  • Giovanni Landi
    • 2
    • 3
  • Andrzej Sitarz
    • 3
  • Walter van Suijlekom
    • 1
  • Joseph C. Várilly
    • 4
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di TriesteTrieste
  3. 3.INFNSezione di NapoliNapoliItaly
  4. 4.Institute of PhysicsJagiellonian UniversityKrakówPoland

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