A projective Dirac operator on CP^2 within fuzzy geometry

Details A projective Dirac operator on CP^2 within fuzzy geometry A projective Dirac operator on CP^2 within fuzzy geometry

2010-11-02

arxiv.org/abs/1011.0647v2

JHEP 1102:106,2011

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, references added, minor changes

Scientific paper

10.1007/JHEP02(2011)106

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.

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