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Abstract

Regularization of quantum field theories (QFTs) 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 applying this procedure of the four-dimensional CP 2 and its QFTs. CP 2 is not spin, but spin c . Its Dirac operator has many unique features. They are explained and their fuzzy versions are described.