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Register a new userQuantum Kinetic Equation in the Rotating Frame and Chiral Kinetic Theory
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A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is demonstrated that the chiral currents and energy-momentum tensor computed by means of them are consistent with the hydrodynamical results. A new semiclassical covariant chiral transport equation is established by inspecting the equations satisfied by the chiral vector fields. It uniquely provides a new three-dimensional semiclassical chiral kinetic theory possessing a Coriolis force term. The particle number and current densities deduced from this transport equation satisfy the anomalous continuity equation and generate the magnetic and vortical effects correctly.
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Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observers frame.
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/mu)$ expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also show that they give equivalent description of the dynamics of chiral fermions.
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.
We derive a chiral kinetic theory with Landau level basis, which is valid for slow-varying magnetic field with arbitrary magnitude. We apply the new chiral kinetic theory to calculate the electric conductivity transverse to the magnetic field in a magnetized QED and QCD plasma. Under the lowest Landau level approximation and relaxation time approximation, we find the transverse conductivity approaches a constant in the large magnetic field limit and is inversely proportional to the relaxation time. We also obtain a frequency-dependent transverse conductivity in response to a time-dependent electric field. We find a high frequency enhancement in this conductivity.
We derive the chiral kinetic equation in 8 dimensional phase space in non-Abelian $SU(N)$ gauge field within the Wigner function formalism. By using the covariant gradient expansion, we disentangle the Wigner equations in four-vector space up to the first order and find that only the time-like component of the chiral Wigner function is independent while other components can be explicit derivative. After further decomposing the Wigner function or equations in color space, we present the non-Abelian covariant chiral kinetic equation for the color singlet and multiplet phase-space distribution functions. These phase-space distribution functions have non-trivial Lorentz transformation rules when we define them in different reference frames. The chiral anomaly from non-Abelian gauge field arises naturally from the Berry monopole in Euclidian momentum space in the vacuum or Dirac sea contribution. The anomalous currents as non-Abelian counterparts of chiral magnetic effect and chiral vortical effect have also been derived from the non-Abelian chiral kinetic equation.
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