論文

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.

In the presence of the fluid helicity v·ω, the magnetic field induces an electric current of the form j=C_{HME}(v·ω)B. This is the helical magnetic effect (HME). We show that for massless Dirac fermions with charge e=1, the transport coefficient CHME is fixed by the chiral anomaly coefficient C=1/(2π^2) as C_{HME}=C/2 independently of interactions. We show the conjecture that the coefficient of the magnetovorticity coupling for the local vector charge, n=CBωB·ω, is related to the chiral anomaly coefficient as CBω=C/2. We also discuss the condition for the emergence of the helical plasma instability that originates from the HME.

We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar SU(N ) gauge theories by calculating the β function of the gauge coupling in arbitrary dimension d based on two different regularization schemes. We find that in d = 3, due to gluon fluctuation effects, the β function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.

We numerically study the chiral turbulence of rotating neutrino matter in the core of supernovae. The rotation yields inverse cascade and the novel current along the direction of rotation called the chiral vortical effect. We for the first time demonstrate that the chiral vortical effect induces a flow in the direction of vorticity and a conversion from fluid helicity to neutrino density. These results may potentially lead to asymmetrical supernova explosions and the increase in the explosion energy in three-dimensional simulations.

In massless QCD coupled to QED in an external magnetic field, a photon with the linear polarization in the direction of the external magnetic field mixes with the charge neutral pion through the triangle anomaly, leading to one gapless mode with the quadratic dispersion relation ω∼k2 and one gapped mode. We show that this gapless mode can be interpreted as the so-called type-B Nambu-Goldstone (NG) mode associated with the spontaneous breaking of generalized global symmetries and that its presence is solely dictated by the anomalous commutator in the symmetry algebra. We also argue a possible realization of such nonrelativistic NG modes in 3-dimensional Dirac semimetals.

We construct the chiral radiation transport equation for left-handed neutrinos in the context of radiation hydrodynamics for core-collapse supernovae. Based on the chiral kinetic theory incorporating quantum corrections due to the chirality of fermions, we derive a general relativistic form of the chiral transfer equation with collisions. We show that such quantum corrections explicitly break the spherical symmetry and axisymmetry of the system. In the inertial frame, in particular, we find that the so-called side jump leads to quantum corrections in the collisions between neutrinos and matter. We also derive analytic forms of such corrections in the emission and absorption rates for the neutrino absorption process. These corrections result in the generation of kinetic helicity and cross helicity of matter, which should then modify the subsequent evolution of matter. This theoretical framework can be applied to investigate the impacts of the chirality of neutrinos on the evolution of core-collapse supernovae.