As before, this is also equivalent to four copies of the Dirac equation. In the abelian case A = e A μ μ d x μ μ , while in the non-abelian case there are additional color indices. The Dirac–Kähler fermion Φ Φ also picks up color indices, with it formally corresponding to cross-sections of the Whitney product of the Atiyah–Kähler bundle of differential forms with the vector bundle of local color spaces.