Abstract
The spin Hall effect of light attracted enormous attention in the literature due to the ongoing progress in developing of new optically active materials and metamaterials with non-trivial spin-orbit interaction. Recently, it was shown that rotating fermionic systems with relativistic massless spectrum may exhibit a 3-dimensional analogue of the spin Hall current — the chiral vortical effect (CVE). Here we show that CVE is a general feature of massless particles with an arbitrary spin. We derive the semi-classical equations of motion in rotating frame from the first principles and show how by coordinate transformation in the phase space it can be brought to the intuitive form proposed in [1]. Our finding clarifies the superficial discrepancies in different formulations of the chiral kinetic theory for rotating systems. We then generalize the chiral kinetic theory, originally introduced for fermions, to an arbitrary spin and study chirality current in a general rotating chiral medium. We stress that the higher-spin realizations of CVE can be in principle observed in various setups including table-top experiments on quantum optics.
Highlights
JHEP03(2019)084 an example of chiral effects for higher spin fields was proposed in [22]
The authors derived an analogue of the chiral vortical effect (CVE) for vector bosons which corresponds to a polarization current in a rotating thermal medium along the angular velocity
We have developed a semi-classical framework for massless particles of arbitrary spin s ≥ 1/2 in rotating frame
Summary
Let us start with a brief review of the Berry phase for particles of an arbitrary spin by using the path integral formalism, see e.g. [1, 23, 41, 42]. 1 2 and higher spins, it is instructive to highlight the similarity in the behavior of the general semi-classical action under Lorentz transformations which are known to be modified by the topological phase. An infinitesimal Lorentz boost should leave the semi-classical action invariant if one ignores the topological phase in eq (2.7), see [18, 44, 45]. Despite that the generalization is straightforward due to the analogy between semiclassical actions for chiral massless particles of different spins, let us briefly describe the angular momentum conservation known to be non-trivial in the fermionic case. The new Lorentz transformation (2.11) contains a shift of the trajectories leading to a non-zero orbital contribution to the full angular momentum in the final state which exactly compensates the spin contribution in the boosted frame. [18, 44]
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