A weak matrix regularization of any single-Casimir level set of a compact semisimple Lie algebra is built from reducible representations whose coadjoint orbits densely fill the variety, with fuzzy S^7 worked out explicitly.
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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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Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy $S^7$ and Beyond
A weak matrix regularization of any single-Casimir level set of a compact semisimple Lie algebra is built from reducible representations whose coadjoint orbits densely fill the variety, with fuzzy S^7 worked out explicitly.