Abstract
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. We calculated the Abelian Berry curvature in lattice QCD.
Highlights
The geometric phase known as the Berry phase [1] is universal in physics
The Berry phase is defined by the change of wave functions in a cyclic adiabatic evolution
In a cyclic adiabatic case, this phase factor cannot be removed by choosing different paths C in parameter space, and, is gauge-invariant
Summary
The geometric phase known as the Berry phase [1] is universal in physics. The Berry phase is defined by the change of wave functions in a cyclic adiabatic evolution. A charge current can be induced by magnetic fields in the presence of imbalanced chiralities of Weyl fermions, which was confirmed in quantum field theory [7, 8], in relativistic hydrodynamics [9, 10, 11, 12], in the holographic models [13, 14, 15, 16], and in lattice quantum chromodynamics (QCD) simulations [17, 18, 19, 20, 21, 22] Those studies have drawn lots of attentions both in high energy physics and in condensed matter physics.
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