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Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential

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Abstract

We consider nonperturbative vacuum polarization effects in the supercritical region for a planar Dirac–Coulomb system with a supercritical extended axially symmetric Coulomb source with a charge \(Z > Z_{{\rm cr},1}\) and radius \(R_0\) in the magnetic field with an axial-vector potential. We study the behavior of the vacuum charge and vacuum current densities, \(\rho_{\mathrm{VP}}(\vec r\,)\) and \(\vec{j}_{\mathrm{VP}}(\vec r\,)\). We focus on the divergence in the theory corresponding to the renormalization and convergence of partial series for \(\rho_{\mathrm{VP}}(\vec r\,)\) and \(\vec{j}_{\mathrm{VP}}(\vec r\,)\). We stress that in contrast to the vacuum charge density, the partial channels with large values of the third projection of the total angular momentum \(|m_j|\) must be taken into account in calculating the vacuum current density in the presence of an external magnetic field localized in the range \(R_1>R_0\). We show that in the presence of a supercritical Coulomb source, the induced magnetic field can enhance the original magnetic field for certain values of parameters of the external vector potential.

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Acknowledgments

The authors thank Professor K. A. Sveshnikov (Faculty of Physics, Moscow State University) for stating the problem and P. A. Grashin (Faculty of Physics, Moscow State University) for the useful discussions.

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Authors and Affiliations

  1. Emanuel Institute of Biochemical Physics, RAS, Moscow, Russia

    A. S. Davydov & V. A. Kuz’min

  2. State Research Center — Burnasyan Federal Medical Biophysical Center of Federal Medical Biological Agency, Moscow, Russia

    A. S. Davydov

  3. Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

    A. A. Krasnov

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  1. A. S. Davydov
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  2. A. A. Krasnov
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  3. V. A. Kuz’min
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Correspondence to A. S. Davydov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 208, pp. 122-144 https://doi.org/10.4213/tmf10048.

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Davydov, A.S., Krasnov, A.A. & Kuz’min, V.A. Vacuum charge and current densities in the supercritical two-dimensional Dirac–Coulomb system in a magnetic field with an axial-vector potential. Theor Math Phys 208, 958–976 (2021). https://doi.org/10.1134/S0040577921070096

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