The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the perturbative solution of Wigner functions play a significant role for the derivation. Moreover, such terms manifest the breaking of Lorentz symmetry for distribution functions. The Lorentz covariance of Wigner functions thus leads to modified Lorentz transformation associated with sidejump phenomena further influenced by background fields and collisions.Introduction.-Novel quantum transport processes in Weyl fermionic systems have been widely investigated, in particular for the so-called chiral magnetic and vortical effects such that charged currents are induced by magnetic and vortical fields [1-3]. These effects associated with quantum anomaly have been studied from different theoretical approaches including relativistic hydrodynamics [4][5][6][7], lattice simulations [8][9][10][11][12], and gauge/gravity duality [13][14][15]. These effects might be (in-)directly observed in heavy ion collisions [16] and in condensed matter systems such as Weyl semimetals [17].From both theoretical and experimental perspectives, it is imperative to understand these anomalous effects in non-equilibrium conditions. One promising approach is kinetic theory, which can delineate non-equilibrium transport of a particle when the interaction and background fields are sufficiently weak. Nevertheless, it is hard to incorporate anomalous effects through the standard Boltzmann equations [6]. The chiral kinetic theory (CKT), which describes anomalous transport of Weyl fermions, has been thus developed from the path-integral [18], Hamiltonian [19], and local-equilibrium quantum kinetic approaches [20,21]. In such formalism, the effective velocity and forces for a single particle are modified by the Berry curvature Ω p = p/(2|p| 3 ), where p represents the spatial momentum of the particle, which originates from the Berry phase in an adiabatic process [22]. Further generalization to massive Dirac fermions can be found in Ref. [23]. In order to bridge the semi-classical approaches [18,19] and quantum field theories, the CKT is also derived from Wigner functions in the high-density effective theory [24] (see also Ref. [25] for relevant study of the on-shell effective field theory.)However, there still exist potential issues in the chiral kinetic equation. First, the field-theory derivation in Refs.[24] and [20,21] are subject to a predominant chemical potential and local equilibrium, respectively. The derivation for more general systems beyond local equilibrium is thus needed. Second, the non-manifestation of Lorentz invariance in the chiral kinetic equation has been recently discussed in Refs. [26,27] from the semi-

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be non-trivially introduced in a co-moving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

We derive the quantum kinetic theory for fermions with arbitrary mass in a background electromagnetic field from the Wigner-function approach. Since spin of massive fermions is a dynamical degree of freedom, the kinetic equations with the leading-order quantum corrections describe entangled dynamics of not only the vector-and axial-charge distributions but also of the spin polarization. Therefore, we obtain one scalar and one axial-vector kinetic equations with magnetization currents pertinent to the spin-orbit interaction. We show that our results smoothly reduce to the massless limit where the spin of massless fermions is no longer an independent dynamical degree of freedom but is enslaved by the chirality and momentum and the accordingly kinetic equations turn into the chiral kinetic theory for Weyl fermions. We provide a kinetic theory covering both the massive and massless cases, and hence resolves the problem in constructing the bridge between them. Such generalization may be crucial for applications to various physical systems. Based on our kinetic equations, we discuss the anomalous currents transported by massive fermions in thermal equilibrium.

It has been suggested that the production of a heavy quarkonium near threshold in electronproton scattering can shed light on the origin of the proton mass via the QCD trace anomaly. We study the photoproduction of J/ψ off the proton using gauge/string duality and demonstrate that the t-dependence of the differential cross section dσ/dt at small-t is a sensitive probe of the trace anomaly.