A projective Dirac operator on CP² within fuzzy geometry

الأصل · EN

We propose an ansatz for the commutative canonical spinc Dirac operator on CP² 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 spinc 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 CP²F based on the fuzzy analogue of the unprojected spinc bundle to show that our commutative projected spinc bundle has the correct SU(3)-representation content.