Abstract
We investigate the effect of an applied constant and uniform magnetic field in the fine-structure constant of massive and massless QED. In massive QED, it is shown that a strong magnetic field removes the so called Landau pole and that the fine-structure constant becomes anisotropic having different values along and transverse to the field direction. Contrary to other results in the literature, we find that the anisotropic fine-structure constant always decreases with the field. We also study the effect of the running of the coupling constant with the magnetic field on the electron mass. We find that in both cases of massive and massless QED, the electron dynamical mass always decreases with the magnetic field, what can be interpreted as an inverse magnetic catalysis effect.
Highlights
The effect of magnetic fields on the different properties of quantum particles has always attracted great interest [1]
Taking into account that the critical temperature to regain the chiral symmetry in the system, Tc, is proportional to the value of the electron dynamical mass at zero temperature [24], we have that the decrease of mdyn with the magnetic field will produce a decrease of Tc, which is the typical behavior of the inverse magnetic catalysis” (IMC) phenomenon in QCD [25]
In this paper we are in particular interested in the effect of an applied uniform and constant magnetic field in the fine-structure constant and into the electron mass in two cases: in normal QED, where there is a different from zero electron mass that can be affected by a magnetic field through radiative corrections, and in massless QED, where the electron mass can be dynamical generated by the so called MCχSB phenomenon [9,10,11,12,13,14,15]
Summary
The effect of magnetic fields on the different properties of quantum particles has always attracted great interest [1]. The paper is organized as follows: In Sec. II, we calculate the Coulomb potential energy in the presence of a constant and uniform magnetic field considering oneloop corrections through the polarization operator in the two limits of strong and weak magnetic fields. IV, we investigate how the magnetic field affects the electron mass in massive QED, as well as in the massless case where the MCχSB phenomenon plays a fundamental role In this analysis, an important new element is that the effect of the magnetic field in the fine-structure constant for each case is included. [29] to study the Coulomb potential in the presence of a magnetic field To have this explicit derivations will serve to make it clear what is the source of the discrepancies with previous results regarding the behavior of the fine-structure constant with the magnetic field [4,5]. We will consider the polarization operator in the one-loop approximation taken in the two extreme values of the magnetic field
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