Abstract
We study the question if a helicity transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant "zilch" current. In order to avoid problems of causality, we quantize the system on a cylinder of a finite radius and then discuss the limit of infinite radius. We find that net helicity- and zilch currents are only generated in the case of the finite radius and are due to duality violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.
Highlights
The quantum field theory of chiral fermions predicts a number of exotic transport phenomena such as the generation of a current in a magnetic field or under rotation
We have studied helicity and zilch photonic currents in the free Maxwell theory induced by rotation in a bounded cylindrical domain
The values of the helicity and zilch photonic currents for both types of boundaries are the same because these boundary conditions are exchanged under a discrete electric-magnetic duality transformation while all expressions of interest are duality invariant
Summary
The quantum field theory of chiral fermions predicts a number of exotic transport phenomena such as the generation of a current in a magnetic field or under rotation. Following the nomenclature introduced by Lipkin these charges are known as “zilches.” For monochromatic light, there is a relation between Lipkin’s original zilch and the optical helicity [27], they are quantities with different properties: while the optical helicity is the generator of the electric-magnetic duality transformations [28], the zilch generates a more complex transformation, involving extra derivatives [29]. We calculate the thermal averages for the optical helicity current and zilch current along the direction of rotation and study the infinite-space limit. The physical significance of such a finite result for the photonic CVE is questionable since the resulting integrals for the thermal averages are mathematically well defined only in the strict case jΩj þ ε 1⁄4 1=R with ε > 0 This requirement means that the zero-rotation limit, Ω → 0, should precede the infinite-volume limit R → ∞.
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