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Lessons from the Klein paradox

E. T. Akhmedov1,2,*, D. V. Diakonov1,4,†, V. I. Lapushkin1,‡, and D. I. Sadekov1,3,§

  • *Contact author: akhmedov@itep.ru
  • †Contact author: dmitrii.dyakonov@phystech.edu
  • ‡Contact author: volapushkin@gmail.com
  • §Contact author: sadekov.di@phystech.edu
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Phys. Rev. D 113, 085016 – Published 22 April, 2026

DOI: https://doi.org/10.1103/1mb6-7hb4

This article was published on 5 October, 2026. Please update your links.

Abstract

We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong steplike electric potential in 1+1 dimensions. First, for a constant (eternal) potential, we calculate the current for different Fock space ground states corresponding to distinct mode bases. While one basis yields a zero current, another produces the standard nonzero value. We then consider a potential that is rapidly switched on, recovering the standard current in the asymptotic future. This result is generalized to potentials that interpolate between different constant values at spatial infinity. Finally, we analyze a potential acting for a finite duration and again reproduce the standard current. A physical interpretation of these results is provided.

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References (18)

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Phys. Rev. D 113, 085016– Published 22 April, 2026
  • Received 3 January 2026
  • Accepted 31 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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