2003/04/06 by V. P. Gusynin, V. A. Miransky, I. A. Shovkovy · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Constant (computer programming) #Coupling (piping) #Coupling constant #Cutoff #Dynamics (music) #Fermion #Fixed point #High-Energy Particle Collisions Research #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-ph
paper · pdf · doi:10.1103/physrevd.67.107703
published as Phys.Rev. D67 (2003) 107703 · 4 pages, REVTeX
arxiv created 2003/04/06 · openalex publication_date 2003/05/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of 1/N expansion. The existence of a threshold value Nthr, dividing the theories with essentially different dynamics, is established. For the number of flavors N\ensuremath≪Nthr, the dynamical mass is very sensitive to the value of the coupling constant \ensuremathαb, related to the magnetic scale \ensuremathμ=√(|eB|). For N of the order of Nthr or larger, a dynamics similar to that in the Nambu--Jona-Lasinio model with a cutoff of the order of √(|eB|) and the dimensional coupling constant G\ensuremath∼1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially \ensuremathαb independent (the dynamics with an infrared stable fixed point). The value of Nthr separates a weak coupling dynamics (with \stackrel\ifmmode \else \~\fi\ensuremathαb\ensuremath≡N\ensuremathαb\ensuremath≪1) from a strong coupling one (with \stackrel\ifmmode \else \~\fi\ensuremathαb\ensuremath\gtrsim1) and is of the order of 1/\ensuremathαb.