Abelian and non-Abelian Berry curvatures in lattice QCD

Understand

We studied the Berry curvature of the massive Dirac fermion in 3+1 dimensions.

• For the non-interacting Dirac fermion, the Berry curvature is non-Abelian because of the degeneracy of positive and negative helicity modes.
• We calculated the non-Abelian Berry curvature analytically and numerically.
• For the interacting Dirac fermion in QCD, the degeneracy is lost because gluons carry helicity and color charge.