Abstract
We derive the Wigner functions of polarized photons in the Coulomb gauge with the ħ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.
Highlights
Generic quantum kinetic theory (QKT) for non-equilibrium many-body photons with collisional effects has not been well established based on the underlying quantum field theory — quantum electrodynamics (QED)
By exploiting the spinor-helicity formalism to write the covariant form of polarization vectors for right/left-handed photons [56,57,58,59], we explicitly derive the Wigner functions up to O( ) in the Coulomb gauge, which manifest how the Berry connections are encoded in distribution functions as the case for Weyl fermions
By using the real-time formalism and adopting a specific power counting scheme, we further construct the general form of the effective QKT for polarized photons with the collision term characterized by self-energies, similar to the fermionic case in ref. [60]
Summary
Let us first briefly recapitulate essential parts of the so-called spinor-helicity formalism [56–. The basic idea of this formalism is to express spin-one vector fields as bispinors since they transform in the (1/2, 1/2) representation of the Lorentz group. As we will show below, this formalism naturally allows us to obtain the result of the quantum kinetic theory for spin-one photons in the same form as that for fermions. In this formalism, the polarization vectors of photons are written with fermion spinors as [56,57,58]. We may denote cR(p) = c(R+) and cR(k) = c(R−) for convenience, where we use the indices “(±)” to represent the eigenvectors of right-handed fermions with positive and negative energies, respectively.
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