Abstract
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 observer's frame.
Highlights
Quantum anomaly is a prominent concept in the transport phenomena of chiral fermions
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
We extended the framework of the chiral kinetic theory (CKT) to curved spacetime, based on quantum field theory
Summary
Quantum anomaly is a prominent concept in the transport phenomena of chiral fermions. Various aspects of the CKT were investigated, including the Lorentz covariance [22,23,26,27], consistent versus covariant anomalies [28,29], particle collisions [22,27,30,31], etc Despite these developments, so far the CKT is restricted to flat spacetime and not conventional to explore the. We derive the CKT in an arbitrary curved spacetime and external electromagnetic field, based on the Wigner function formalism that respects the U(1) gauge invariance, and the local Lorentz and diffeomorphism covariance [40,41,42]. We can regard pμ and yμ as “x-independent” variables under the parallel transport by
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