Comment on "modified Coulomb law in a strongly magnetized vacuum".
In a recent Letter , Shabad and Usov studied the electric potential of a charge placed in a strong magnetic field B ≫ B0 ≡ m/e (m is the electron mass and e is its charge), as modified by the vacuum polarization. According to these authors, in the limit B → ∞ the modified potential becomes a Dirac delta function plus a regular background. With this potential they showed that the unboundedness from below of the nonrelativistic hydrogen spectrum is removed. In this Comment, we point out that Shabad and Usov used an incorrect calculation to arrive at their, otherwise, correct result and conclusion. It is firmly established that the magnetic catalysis of chiral symmetry breaking  is a universal phenomenon. The general result states that a strong magnetic field leads to the generation of a dynamical fermion mass even at the weakest attractive interaction between fermions. The realization of this phenomenon in the chiral limit in QED has been studied in detail in the literature [3, 4, 5]. In particular, in Ref. , we obtained an asymptotic expression for the dynamical fermion mass, reliable in the weak coupling regime and the strong field approximation. The dynamical fermion mass in massless QED in a strong magnetic field, mdyn, is given by

title: REAL-TIME NONEQUILIBRIUM DYNAMICS IN HOT QED PLASMAS
abstract: The quantum kinetics of photons in hot QED plasmas is studied directly in real time by implementing the dynamical renormalization group. In contrast to conventional approach, the dynamical renormalization group method consistently includes off-shell (energy non-conserving) effects and accounts for time-dependent collisional kernel. To lowest order we find that in the relaxation time approximation the semihard photon distribution function relaxes with a power law.

title: Nonequilibrium relaxation of Bose-Einstein condensates: Real-time equations of motion and Ward identities
abstract: We present a field-theoretical method to obtain consistently the equations of motion for small amplitude condensate perturbations in a homogeneous Bose-condensed gas directly in real time. It is based on a linear response and combines the Schwinger–Keldysh formulation of nonequilibrium quantum field theory with the Nambu–Gor'kov formalism of quasiparticle excitations in the condensed phase and the tadpole method in quantum field theory. This method leads to causal equations of motion that allow us to study the nonequilibrium evolution as an initial value problem. It also allows us to extract directly the Ward identities, which are a consequence of the underlying gauge symmetry and which in equilibrium lead to the Hugenholtz–Pines theorem. An explicit one-loop calculation of the equations of motion beyond the Hartree–Fock–Bogoliubov approximation reveals that the nonlocal, absorptive contributions to the self-energies corresponding to the Beliaev and Landau damping processes are necessary to fulfill the Ward identities in or out of equilibrium. It is argued that a consistent implementation at low temperatures must be based on the loop expansion, which is shown to fulfill the Ward identities order by order in perturbation theory.

title: Real time nonequilibrium dynamics in hot QED plasmas: Dynamical renormalization group approach
abstract: We study the real-time nonequilibrium dynamics in hot QED plasmas implementing a dynamical renormalization group and using the hard thermal loop (HTL) approximation. The focus is on the study of the relaxation of gauge and fermionic mean fields and on the quantum kinetics of the photon and fermion distribution functions. For semihard photons of momentum eT q \gamma and \bar{q} -> \bar{q}\gamma) at O(\alpha) grows logarithmically in time and is comparable to that produced from on-shell Compton scattering and pair annihilation at O(\alpha \alpha_s). Fermion mean fields relax as e^{-\alpha T t ln(\omega_P t)} with \omega_P=eT/3 the plasma frequency, as a consequence of the emission and absorption of soft magnetic photons. A quantum kinetic equation for hard fermions is obtained directly in real time from a field theoretical approach improved by the dynamical renormalization group. The collision kernel is time-dependent and infrared finite.

title: PROGRESS ON CHIRAL SYMMETRY BREAKING IN A STRONG MAGNETIC FIELD
abstract: The problem of chiral symmetry breaking in QED in a strong magnetic field is briefly reviewed. Recent progress on issues regarding the gauge fixing independence of the dynamically generated fermion mass is discussed.

title: Dynamical electron mass in a strong magnetic field
abstract: Motivated by recent interest in understanding properties of strongly magnetized matter, we study the dynamical electron mass generated through approximate chiral symmetry breaking in QED in a strong magnetic field. We reliably calculate the dynamical electron mass by numerically solving the nonperturbative Schwinger-Dyson equations in a consistent truncation within the lowest Landau level approximation. It is shown that the generation of dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass that explicitly breaks chiral symmetry in the absence of a magnetic field.

title: THE PROPOSED EXPERIMENTAL STUDY ON BEAM-PHOTOELECTRON INTERACTIONS IN BEPC
abstract: A vertical collective effect suspected as photoelectron instability (PEI) has been observed at Photon Factory (PF) of KEK in recent years. This phenomena may impose a limitation on the performance of the proposed B-Factories or T-c Factories. An experiment has been planned to test it using positron beam at Beijing Electron Positron Collider (BEPC) in 1996 under the cooperation between IHEP and KEK. Preliminary simulation results have shown that the PEI may occur in BEPC on the total beam current level of 40 mA over more than 20 bunches. The instrumentation for observation of PEI is jointly prepared by both sides of IHEP and KEK. The machine study has been scheduled and the experiment will progress under the conditions of the best machine performance.

title: AGE AND STRUCTURE PARAMETERS OF THE REMOTE M31 GLOBULAR CLUSTER B514 BASED ON HST, 2MASS, GALEX, AND BATC OBSERVATIONS
abstract: B514 is a remote M31 globular cluster (GC) which is located at a projected distance of Rp 55 kpc. Deep observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate integrated light and star counts of B514. By coupling the analysis of the distribution of the integrated light with star counts, we are able to reliably follow the profile of the cluster out to ~40''. Based on the combined profile, we study in detail its surface brightness distribution in the F606W and F814W filters and determine its structural parameters by fitting a single-mass isotropic King model. The results showed that the surface brightness distribution departs from the best-fit King model for r > 10''. B514 is quite flat in the inner region and has a larger half-light radius than the majority of normal GCs of the same luminosity. It is interesting that, in the MV versus log Rh plane, B514 lies nearly on the threshold for ordinary GCs as defined by Mackey & van den Bergh. In addition, B514 was observed as part of the Beijing-Arizona-Taiwan-Connecticut (BATC) Multicolor Sky Survey, using 13 intermediate-band filters covering a wavelength range of 3000-8500 A. Based on aperture photometry, we obtain its spectral energy distributions (SEDs) as defined by the 13 BATC filters. We determine the cluster's age and mass by comparing its SEDs (from 2267 to 20000 A, comprised of photometric data from the near-ultraviolet band of the Galaxy Evolution Explorer, 5 Sloan Digital Sky Survey bands, 13 BATC intermediate-band filters, and Two Micron All Sky Survey near-infrared JHK s filters) with theoretical stellar population synthesis models, resulting in an age of 11.5 ± 3.5 Gyr. This age confirms the previous suggestion that B514 is an old GC in M31. B514 has a mass of 0.96-1.08 × 106 M ☉ and is a medium-mass GC in M31.

title: STRUCTURAL PARAMETERS FOR GLOBULAR CLUSTERS IN THE OUTER HALO OF M31
abstract: In this paper, we present internal surface brightness profiles, using images in the F606W and F814W filter bands observed with the Advanced Camera for Surveys on the Hubble Space Telescope, for 10 globular clusters (GCs) in the outer halo of M31. Standard King models are fitted to the profiles to derive their structural and dynamical parameters. The results show that, in general, the properties of clusters in M31 and the Milky Way fall in the same regions of parameter spaces. The outer halo GCs of M31 have larger ellipticities than most of the GCs in M31 and the Milky Way. Their large ellipticities may be due to galaxy tides coming from satellite dwarf galaxies of M31 or may be related to the apparently more vigorous accretion or merger history that M31 has experienced. The tight correlation of cluster binding energy E{sub b} with mass M{sub mod} indicates that the 'fundamental plane' does exist for clusters, regardless of their host environments, which is consistent with previous studies.

title: PROTON BRANCH OF MODIFIED URCA PROCESS IN STRONG MAGNETIC FIELD AND SUPERFLUIDITY OF NEUTRON STAR CORES
abstract: The modified URCA process produces efficient neutrino energy losses in neutron star cores, and has been shown to go via neutron and proton branches. Based on the improved electron chemical potential and critical temperature of superfluidity, the effects of strong magnetic field and superfluidity on the proton branch of modified URCA process are investigated simultaneously in this paper. The results show that strong magnetic field enhances the neutrino emissivities compared to the case in zero magnetic field, and superfluidity reduces the emissivities significantly. For the total neutrino emissivities, the magnetic field is dominant at the initial stage of neutron star cooling, but the superfluidity becomes crucial as the temperature drops below the critical temperature.

title: Vorticity and magnetic field production in relativistic ideal fluids
abstract: In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogeneous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe.