• DOI:10.1103/PhysRevLett.99.228901
• Corpus ID: 22652634

Comment on "modified Coulomb law in a strongly magnetized vacuum".

@article{Wang2007CommentO,
  title={Comment on "modified Coulomb law in a strongly magnetized vacuum".},
  author={Shangyun Wang},
  journal={Physical review letters},
  year={2007},
  volume={99 22},
  pages={
          228901; author reply 228902
        }
}

• Shangyun Wang
• Published 11 October 2007
• Physics
• Physical review letters

In a recent Letter [1], 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 [2] 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. [5], 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 [5]