It was recently conjectured by Shabad and Usov that there exists in QED a maximum magnetic field of 10^42 Gauss, above which the magnetized vacuum becomes unstable. Using a nonperturbative analysis that consistently incorporates the effective electron mass and the screening effect in a strong magnetic field, we show that the conjectured phenomenon of positronium collapse never takes place. Thus, there does not exist a maximum magnetic field in QED and the magnetized vacuum is stable for all values of the magnetic field.
So the answer of the maximum magnetic field is not 42 (10 to the 42 Gauss).
Shabad and Usov considered a positronium (i.e., an electron-positron bound state) placed in a strong magnetic field, and found that the magnetic field significantly enhances the Coulomb attraction between the constituent electron and positron. The Coulomb attraction becomes stronger and stronger until the electron and positron fall onto each other at the maximum magnetic field of 10^42 G. The maximum magnetic field of
10^42 G, if correct, would rule out the existence of extremely strong magnetic fields of 10^47 − 10^48 G in the vicinity of superconductive cosmic strings, and, most importantly, the exceeding of which would cause the restructuring of the strongly magnetized vacuum, thus calling for a revision of QED.
Conclusion of this paper – Positronium is unambiguously identified as the (pseudo) Nambu-Goldstone boson for spontaneous (explicit) chiral symmetry breaking in massless (massive) QED in a strong magnetic field. It is shown that the phenomenon of positronium collapse conjectured by Shabad and Usov never takes place. Consequently, there does not exist a maximum magnetic field in QED and the magnetized vacuum is stable for all values of the magnetic field.
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