Fuzzy CP2

2001/03/31 by G. Alexanian, A. P. Balachandran, G. Immirzi +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #gr-qc #hep-lat #math.QA

paper · pdf · doi:10.1016/s0393-0440(01)00070-5

published as J.Geom.Phys.42:28-53,2002 · 32 pages,LaTeX; References added and several typos corrected

arxiv created 2001/04/11 · arxiv updated 2009/11/30

Abstract

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this paper, we report on our work on the ``fuzzification'' of the four-dimensional CP2 and its QFT's. CP2 is not spin, but spin_c. Its Dirac operator has many unique features. They are explained and their fuzzy versions are described.

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