Abstract
We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz frame. We reveal that on top of this conventional frame choosing vector, higher-order quantum correction to the chiral kinetic theory brings an additional degrees of freedom to specify the distribution function. Based on this framework, we derive new types of fermionic transport, that is, the charge current and energy-momentum tensor induced by the gravitational Riemann curvature. Such novel phenomena arise not only under genuine gravity but also in a (pseudo-)relativistic fluid, for which inhomogeneous vorticity or temperature are effectively represented by spacetime metric tensor. It is especially found that the charge and energy currents are antiparallelly induced by an inhomogeneous fluid vorticity (more generally, by the Ricci tensor R0i), as a consequence of the spin-curvature coupling. We also briefly discuss possible applications to Weyl/Dirac semimetals and heavy-ion collision experiments.
Highlights
Created in relativistic heavy-ion collision experiments [7]
We reveal that on top of this conventional frame choosing vector, higher-order quantum correction to the chiral kinetic theory brings an additional degrees of freedom to specify the distribution function
The so-called chiral kinetic theory (CKT) [20, 21], which nicely reproduces the chiral anomaly, plays a pivotal role in the development of various studies of the chiral transport phenomena [22,23,24,25,26,27,28,29,30,31,32,33,34,35,36] in the context of heavy-ion collision, condensed matter and neutrino physics; the kinetic theory is inapplicable to strongly-coupled quark-gluon plasmas, the early stage of heavy-ion collisions is described well by the Boltzmann transport theory [37,38,39]
Summary
In the evaluation of physical quantities such as eq (2.43), it is necessary to identify the explicit form of f(0),(1),(2) For this purpose, the frame (i.e., nμ and uμ) dependences of Rμ are a crucial concept; as shown below, we derive a constraint on the distribution function from the proper transformation law under the shift of the frames. The transformation laws under the change of the frames nμ and uμ are helpful to identify the equilibrium distribution function. This is a plausible form in the sense that the spin-vorticity coupling term is correctly reproduced: f(0) + f(1) f(0)(g(0) + 2 Σμnν ∇μβν ) + O( 2) In this case, the first order Wigner function (2.28) is written as.
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