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Does Schwinger's value for the current of created pairs gets modified for long and strong enough pulse?

E. T. Akhmedov, P. S. Zavgorodny

TL;DR

The work addresses whether Schwinger's predicted current for vacuum pair creation is modified by long, strong electric pulses. By combining semiclassical WKB mode analysis with Schwinger–Keldysh diagrammatics in a weak-field scalar QED setup, it first reproduces the tree-level current and then probes loop corrections. The main finding is that while the tree-level current retains Schwinger's form with a refined prefactor, the leading two-loop correction grows as $T^4$ and, for sufficiently long pulses, can dominate, signaling a potential avalanche mechanism and the necessity of resummation near the Schwinger limit. These results illuminate the nonperturbative dynamics of pair production in nonstationary backgrounds and have implications for early-universe backreaction and strong-field QED in time-dependent settings.

Abstract

We determine the parametric conditions (pulse strength and duration) under which Schwinger's prediction for the pair-creation current - and therefore the probability - is significantly altered.

Does Schwinger's value for the current of created pairs gets modified for long and strong enough pulse?

TL;DR

The work addresses whether Schwinger's predicted current for vacuum pair creation is modified by long, strong electric pulses. By combining semiclassical WKB mode analysis with Schwinger–Keldysh diagrammatics in a weak-field scalar QED setup, it first reproduces the tree-level current and then probes loop corrections. The main finding is that while the tree-level current retains Schwinger's form with a refined prefactor, the leading two-loop correction grows as and, for sufficiently long pulses, can dominate, signaling a potential avalanche mechanism and the necessity of resummation near the Schwinger limit. These results illuminate the nonperturbative dynamics of pair production in nonstationary backgrounds and have implications for early-universe backreaction and strong-field QED in time-dependent settings.

Abstract

We determine the parametric conditions (pulse strength and duration) under which Schwinger's prediction for the pair-creation current - and therefore the probability - is significantly altered.
Paper Structure (12 sections, 76 equations, 2 figures)

This paper contains 12 sections, 76 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The setup of the problem
  3. Refined expression for the tree-level current
  4. Subleading oscillatory contributions to the tree-level current
  5. General discussion of loop integrals and interrelation of the leading secular contributions to them
  6. One-loop corrections to the photon's propagator in the limit of soft momenta
  7. Two-loop correction to the electric current
  8. Conclusions and acknowledgments
  9. Details of the loop integrals calculation
  10. Calculation of one-loop correction to the photon's propagator in the limit of soft momenta
  11. Calculation of the two-loop correction to $n_\mathbf{p}(T)$
  12. Analysis of subleading contributions

Figures (2)

  • Figure 1: One-loop correction to the photon's propagator. In the Schwinger-Keldysh technique one has a sum of diagrams of such a form with vertexes attributed to different sides of the Keldysh's "closed" time contour.
  • Figure 2: Two-loop diagrams of such a form contain an additional power of growth with $T$. In the Schwinger-Keldysh technique one has a sum of diagrams of such a form with vertexes attributed to different sides of the Keldysh's "closed" time contour.