Dirac sea and chiral anomaly in the quantum kinetic theory

Abstract

We revisit the chiral anomaly in the quantum kinetic theory in the Wigner function formalism under the background field approximation. Our results show that the chiral anomaly is actually from the Dirac sea or the vacuum contribution in the un-normal-ordered Wigner function. We also demonstrate that this contribution modifies the chiral kinetic equation for antiparticles.

Second-order Charge Currents and Stress Tensor in Chiral System

“…Since the Wigner equation was derived from Dirac equation, the bilinear operator in Wigner function must be not normal ordered. It has been demonstrated in [73] that this point plays a central role to give rise to the chiral anomaly in the quantum kinetic theory. We can decompose the Wigner function in terms of 16 independent generators of the Clifford algebra,…”

Chiral Anomaly, Dirac Sea and Berry monopole in Wigner Function Approach

“…As mentioned above, we will consider the specific fermion system near equilibrium. Hence we choose the zeroth order solutions V µ (0) and A µ (0) as equilibrium distribution in free field theory [14,15,10]…”

“…the fluid velocity u µ is uniform. Note that Z v is the vacuum term or Dirac sea term which comes from the anticommutation of creation and annihilation operators of antifermions as described in [10,16,17]. This term is universal and does not depend on the specific distribution n F (x) at all.…”

“…It has been shown in [10] that the Dirac sea or vacuum contribution from the anti-commutation relations between antiparticle field operators in un-normal-ordered Wigner function plays a central role to generate chiral anomaly in quantum kinetic theory both for massive and for massless fermion systems. In this work, we will take a simple and concrete example to illustrate these points.…”

Massless Limit of Transport Theory for Massive Fermions

“…Because these phenomena are closely related to the evolution of quantum systems, kinetic theory is a natural choice to study them [15][16][17][18]. From the Wigner function formalism [19][20][21][22], the kinetic theories of both massive [23][24][25] and massless fermions [26][27][28][29][30][31][32][33][34] are studied. One of the advantages of Wigner function formalism is that it includes spin degree of freedom naturally, which is essential in the study of magnetic field and vorticity related phenomena.…”