Fuzzy CP**2

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 CP 2 and its QFT’s. CP 2 is not spin, but spinc. Its Dirac operator has many unique features. They are explained and their fuzzy versions are described.