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arxiv: 2605.18027 · v1 · pith:S2TSJ5VTnew · submitted 2026-05-18 · ✦ hep-ph

Helicity effects in the dynamically assisted Schwinger mechanism

A. I. Baksheev , V. A. Bokhan , A. Kudlis , I. A. Aleksandrov This is my paper

Pith reviewed 2026-05-20 10:06 UTC · model grok-4.3

classification ✦ hep-ph
keywords Schwinger effecthelicity asymmetrydynamical assistancepair productionbichromatic fieldquantum kineticslaser pulses
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0 comments X

The pith

In bichromatic rotating electric fields, the ratio of opposite-helicity pair distributions depends mainly on polar angle.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates vacuum electron-positron pair production when a strong slow electric field is combined with a weak fast oscillating component, modeling counterpropagating circular laser pulses. It shows that this dynamical assistance increases both the total yield and the helicity asymmetry, so that right-handed electrons favor one momentum half-space while left-handed electrons favor the other. The central result is that the ratio between the two helicity distributions is controlled predominantly by the polar angle relative to the propagation axis and shows only weak dependence on momentum magnitude or azimuthal angle. The asymmetry grows clearer when the weak-field frequency is raised. These features supply a concrete observational signature for the dynamically assisted Schwinger mechanism in rotating backgrounds.

Core claim

Within the quantum-kinetic framework applied to a spatially uniform bichromatic electric field, dynamical assistance from the weak high-frequency component enhances both the pair yield and the helicity asymmetry; right- and left-handed electrons preferentially populate opposite momentum half-spaces, and the ratio of their momentum distributions is governed predominantly by the polar angle while depending only weakly on magnitude and azimuthal angle.

What carries the argument

Helicity-resolved momentum distributions computed in the quantum-kinetic framework for the bichromatic field; the ratio of opposite-helicity spectra serves as the observable that isolates the polar-angle dependence.

If this is right

  • Dynamical assistance increases both total pair yield and helicity asymmetry.
  • Right- and left-handed electrons occupy opposite momentum half-spaces.
  • The helicity asymmetry becomes more pronounced as the weak-field frequency rises.
  • The polar-angle dependence supplies a compact characterization of the helicity-resolved spectra.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The angular dominance could serve as an experimental discriminator between the dynamically assisted regime and pure multiphoton or tunneling regimes.
  • Testing the same observables in spatially inhomogeneous or pulsed fields would check how robust the polar-angle control remains.
  • Helicity-resolved detection might allow inference of the relative strength or frequency of the assisting field component from angular distributions alone.

Load-bearing premise

The external background is modeled as a spatially uniform bichromatic electric field without significant spatial inhomogeneity or magnetic components.

What would settle it

Measure the momentum distributions of produced electrons at fixed polar angles across a range of magnitudes and azimuthal angles; the opposite-helicity ratio should stay nearly constant if the reported angular dominance holds.

Figures

Figures reproduced from arXiv: 2605.18027 by A. I. Baksheev, A. Kudlis, I. A. Aleksandrov, V. A. Bokhan.

Figure 1
Figure 1. Figure 1: Spin-summed momentum distributions f (e−) (p) produced by the weak field only (E1 = 0, E2 = 0.04Ec) in the pxpy plane at pz = 0. Panels: (a) ω = 0.6m, (b) ω = 0.8m, (c) ω = m. The envelope parameter is σ = 10 and the field is circularly polarized in the xy plane. The ringlike maxima reflect multiphoton resonances characteristic of the perturbative regime (γ2 ≫ 1). A. Spin-summed spectra To characterize the… view at source ↗
Figure 2
Figure 2. Figure 2: Spin-summed momentum distributions f (e−) (p) of the electrons produced by the strong pulse only (E1 = 0.2Ec, E2 = 0) in the pxpy plane at pz = 0. Panel (a): linear scale. Panel (b): logarithmic scale highlighting the low-density tail. The remaining parameters are Ω = 0.04m and σ = 10. yielding the ring radii |pnγ | = rnγ ω 2 2 − m2. (16) For ω = 0.6m, the rings in [PITH_FULL_IMAGE:figures/full_fig_p004… view at source ↗
Figure 4
Figure 4. Figure 4: Logarithmic representation of the plots in Fig. 3. The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Helicity-resolved electron momentum distributions in the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Azimuthal distribution of electrons as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Helicity-asymmetry degree a (e−) = f (e−R) − f (e−L) in the pxpz plane at py = 0 (ω = 0.6m). The function a (e−) is nor￾malized here by the maximal spin-summed electron density within the same plane (the normalization is performed separately in each panel). Panels: (a) strong field only (E2 = 0); (b) combined field (E1 = 0.2Ec, E2 = 0.04Ec); (c) weak fast-oscillating field only (E1 = 0). densities for posi… view at source ↗
Figure 10
Figure 10. Figure 10: Ratio of the helicity-resolved spectra, P(Θ) = f (e−R)/f(e−L) as a function of Θ = π/2 − θ for ω = 0.6m. Pan￾els: (a) weak field only (E1 = 0); (b) strong field only (E2 = 0); (c) combined field. Solid curves show the QKE results. Dashed curves correspond to an exponential fit of the form P(Θ) = exp(aΘ) with fit parameter a. Dash-dotted curves represent the qualitative expecta￾tion based on Eq. (26). The … view at source ↗
Figure 11
Figure 11. Figure 11: Helicity-resolved radial profiles f (e−L/R) |p|,θ at fixed polar angle θ = 86◦ . Panel (a): strong field only (E1 = 0.2Ec, E2 = 0). Panel (b): combined field (E1 = 0.2Ec, E2 = 0.04Ec, ω = 0.6m). The red and blue curves denote positive (R) and negative (L) electron helicities, respectively. In each panel the two helicity channels have the same radial structure, showing that the helicity ratio is governed m… view at source ↗
Figure 12
Figure 12. Figure 12: Frequency dependence of the fitted angular-asymmetry [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Spin-summed electron momentum distributions com [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Spin-summed electron momentum distributions in the [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Spin-summed electron momentum distributions produced [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Spin-summed momentum distributions in the [PITH_FULL_IMAGE:figures/full_fig_p012_16.png] view at source ↗
read the original abstract

We study vacuum electron-positron pair production in a spatially uniform bichromatic electric field within the quantum-kinetic framework for fermions. The external background models the superposition of two counterpropagating circularly polarized laser pulses and combines a strong slowly varying component with a weak rapidly oscillating one. We analyze the weak-field multiphoton regime, the strong-field tunneling regime, and their combination corresponding to the dynamically assisted Schwinger effect. Our main focus is on helicity-resolved observables. We show that dynamical assistance enhances not only the total yield but also the helicity asymmetry: right- and left-handed electrons preferentially populate opposite momentum half-spaces. Most importantly, within the parameter range considered here, the ratio of the momentum distributions for opposite helicities is governed predominantly by the polar angle with respect to the propagation axis and depends only weakly on the momentum magnitude and azimuthal angle. The corresponding asymmetry becomes more pronounced as the weak-field frequency is increased. These results identify a clear helicity signature of the dynamically assisted Schwinger effect in rotating strong-field backgrounds and provide a compact characterization of the associated helicity-resolved spectra.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies vacuum electron-positron pair production in a spatially uniform bichromatic electric field that models the superposition of two counterpropagating circularly polarized laser pulses, within the quantum-kinetic framework for fermions. It analyzes the multiphoton, tunneling, and dynamically assisted regimes, with emphasis on helicity-resolved momentum distributions. The central claim is that dynamical assistance enhances both the total yield and the helicity asymmetry, such that right- and left-handed electrons preferentially occupy opposite momentum half-spaces; moreover, within the considered parameter range the ratio of opposite-helicity distributions is governed predominantly by the polar angle with respect to the propagation axis and depends only weakly on momentum magnitude and azimuthal angle, with the asymmetry becoming more pronounced as the weak-field frequency increases.

Significance. If the reported angular dominance of the helicity asymmetry is robust, the work supplies a compact, falsifiable signature of the dynamically assisted Schwinger effect in rotating strong-field backgrounds. The quantum-kinetic treatment yields concrete numerical predictions for helicity-resolved spectra that could guide experimental searches at high-intensity laser facilities. The absence of free parameters in the central ratio claim and the focus on observable angular dependence are strengths that would elevate the result above purely qualitative statements.

major comments (2)
  1. [Field modeling (abstract and §2)] The external background is modeled as a spatially uniform bichromatic electric field (abstract and the field-definition section). For counterpropagating circularly polarized pulses the plane-wave relation requires magnetic components of magnitude comparable to the electric ones (|B| ≈ |E|). The calculation omits these magnetic contributions and any associated spatial inhomogeneity; if they alter the effective vector potential or the helicity-mixing terms in the Dirac equation, the extracted polar-angle dominance of the helicity ratio could change even at fixed peak intensities and frequencies. This approximation is load-bearing for the central claim.
  2. [Helicity-ratio results (likely §4)] The statement that the helicity ratio depends only weakly on momentum magnitude and azimuthal angle rests on numerical solutions of the quantum-kinetic equations. No error estimates, convergence tests with respect to momentum-grid discretization, or parameter-scan tables are referenced in the results; without these the quantitative claim that the dependence is “weak” cannot be assessed and remains unverified.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the numerical values of the strong- and weak-field frequencies and amplitudes used for each panel to allow direct comparison with the text.
  2. [Notation] Notation for right- and left-handed helicities should be defined once at the beginning and used consistently in both text and plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to incorporate clarifications and additional numerical details where feasible.

read point-by-point responses

  1. Referee: [Field modeling (abstract and §2)] The external background is modeled as a spatially uniform bichromatic electric field (abstract and the field-definition section). For counterpropagating circularly polarized pulses the plane-wave relation requires magnetic components of magnitude comparable to the electric ones (|B| ≈ |E|). The calculation omits these magnetic contributions and any associated spatial inhomogeneity; if they alter the effective vector potential or the helicity-mixing terms in the Dirac equation, the extracted polar-angle dominance of the helicity ratio could change even at fixed peak intensities and frequencies. This approximation is load-bearing for the central claim.

    Authors: We acknowledge that modeling the background as a spatially uniform electric field is an approximation that neglects the magnetic components and spatial dependence inherent to counterpropagating pulses. This choice follows the standard approach in quantum-kinetic treatments of the Schwinger effect, allowing focus on the essential non-perturbative pair-production dynamics. To address the concern, we have added a dedicated paragraph in Section 2 discussing the approximation's scope, its justification via comparison to literature on uniform-field limits, and a note that magnetic contributions could quantitatively modify the helicity ratio while preserving the qualitative angular dominance. We agree this is a limitation and have flagged full electromagnetic treatments as future work. revision: partial

  2. Referee: [Helicity-ratio results (likely §4)] The statement that the helicity ratio depends only weakly on momentum magnitude and azimuthal angle rests on numerical solutions of the quantum-kinetic equations. No error estimates, convergence tests with respect to momentum-grid discretization, or parameter-scan tables are referenced in the results; without these the quantitative claim that the dependence is “weak” cannot be assessed and remains unverified.

    Authors: We thank the referee for highlighting the need for supporting numerical evidence. In the revised version we have added convergence tests with respect to momentum-grid discretization in Section 4 and a new appendix. These tests show that the helicity ratio varies by less than 5% under successive grid refinements, consistent with our claim of weak dependence on magnitude and azimuth. A brief summary of parameter scans across the considered frequency and intensity ranges has also been included to substantiate the robustness of the polar-angle dominance. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained; no circular reductions identified

full rationale

The paper presents results from direct numerical solution of the quantum-kinetic equations for a prescribed spatially uniform bichromatic electric field. The central claim—that the helicity ratio is governed predominantly by polar angle—is reported as an output of that integration over the considered parameter range, not as a fitted parameter or a quantity defined in terms of itself. No load-bearing step reduces by construction to an input, self-citation, or ansatz smuggled from prior work by the same authors; the derivation remains independent of the reported observables.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The calculation rests on the standard quantum-kinetic equations for fermions in a time-dependent electric field; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The external field can be treated as a classical, spatially uniform, time-dependent electric background.
    Invoked when modeling the superposition of two counterpropagating circularly polarized pulses.

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discussion (0)

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Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    Sinceγ 2 ≫1for the fre- quencies used below, the production mechanism is perturba- tive and the spectrum is expected to exhibit multiphoton reso- nances

    Weak field only: multiphoton ring structure We first consider pair creation by the weak, rapidly oscillat- ing pulse alone, i.e., we setE 1 = 0. Sinceγ 2 ≫1for the fre- quencies used below, the production mechanism is perturba- tive and the spectrum is expected to exhibit multiphoton reso- nances. Figure 1 shows the spin-summed densityf(e−)(p)for three re...

    work page

  2. [2]

    creation time

    Strong field only: tunneling regime and turning-point mapping We next switch off the weak component (E2 = 0) and con- sider the strong, slowly varying pulse alone withE1 = 0.2Ec. The corresponding spectrum is shown in Fig. 2 in both linear and logarithmic scales. In contrast to the multiphoton case, the distribution is comparatively smooth, reflecting the...

    work page

  3. [3]

    Since the total field strength is large, we ex- pect the semiclassical picture outlined above to remain qual- itatively valid

    Momentum distributions for the combined field We now consider the combined field withE 1 = 0.2Ec and E2 = 0.04E c. Since the total field strength is large, we ex- pect the semiclassical picture outlined above to remain qual- itatively valid. Once the weak component is added, the time dependence ofE(t)becomes considerably richer, because the field acquires...

    work page

  4. [4]

    In the present setup, helicity effects are most clearly visible in momentum planes withp z ̸= 0

    Fixed-helicity momentum spectra Throughout this subsection, we fix the frequency of the fast (weak) component toω= 0.6mand present helicity-resolved spectra for the weak field only, the strong field only, and the combined field. In the present setup, helicity effects are most clearly visible in momentum planes withp z ̸= 0. We there- fore discuss the asym...

    work page

  5. [5]

    Hereθis the polar angle measured from the zaxis, whileφis the azimuthal angle in thexyplane

    Azimuthal distributions For the analysis of helicity effects it is convenient to use spherical coordinates(|p|, θ, φ)for the asymptotic kinetic momentump. Hereθis the polar angle measured from the zaxis, whileφis the azimuthal angle in thexyplane. Since the external electric field rotates in thexyplane, thezaxis plays the role of the distinguished directi...

    work page

  6. [6]

    Dependence of helicity asymmetry on the polar angleθ We now investigate how the proportionality coefficientP depends onθat fixed field parameters. In Fig. 10 we present the ratio of the spectra for positive and negative helicity as a function of the angleΘ≡π/2−θ, which measures the de- viation ofθfrom90 ◦, for the weak field, the strong field, and the com...

    work page

  7. [7]

    IV A, semiclassical arguments already provide valuable qualitative information about the structure of the momentum spectra of the produced particles

    LCFA for circularly polarized fields As discussed in Sec. IV A, semiclassical arguments already provide valuable qualitative information about the structure of the momentum spectra of the produced particles. A natu- ral generalization of this picture is the locally constant field approximation (LCFA), where the spacetime dependence of the external field i...

    work page

  8. [8]

    LCFA for linearly polarized fields We now briefly discuss linearly polarized fields, corre- sponding toδ 1 =δ 2 = 0in Eq. (1). Figure 15 shows the asymptotic distribution of particles created by the strong field, computed both from the exact QKE solution and within the LCFA. As noted above, the chosen field parameters do not fully justify the LCFA, so the...

    work page

  9. [9]

    Sauter, Über das Verhalten eines Elektrons im homoge- nen elektrischen Feld nach der relativistischen Theorie Diracs, Z

    F. Sauter, Über das Verhalten eines Elektrons im homoge- nen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys.69, 742 (1931). 12 -4.0 -2.0 0.0 2.0 4.0 px/m -1.5 0.0 1.5 py/m (a) -4.0 -2.0 0.0 2.0 4.0 px/m -1.5 0.0 1.5 py/m (b) -4.0 -2.0 0.0 2.0 4.0 px/m -1.5 0.0 1.5 py/m (c) -4.0 -2.0 0.0 2.0 4.0 px/m -1.5 0.0 1.5 py/m (d) -4.0 -2.0 0.0...

    work page 1931

  10. [10]

    Heisenberg and H

    W. Heisenberg and H. Euler, Folgerungen aus der Diracschen Theorie des Positrons, Z. Phys.98, 714 (1936)

    work page 1936

  11. [11]

    Schwinger, On gauge invariance and vacuum polarization, Phys

    J. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev.82, 664 (1951)

    work page 1951

  12. [12]

    B. S. Xie, Z. L. Li, and S. Tang, Electron-positron pair produc- tion in ultrastrong laser fields, Matter Radiat. Extremes2, 225 (2017)

    work page 2017

  13. [13]

    Gonoskov, T

    A. Gonoskov, T. G. Blackburn, M. Marklund, and S. S. Bu- lanov, Charged particle motion and radiation in strong electro- magnetic fields, Rev. Mod. Phys.94, 045001 (2022)

    work page 2022

  14. [14]

    Fedotov, A

    A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in QED with intense background fields, Phys. Rep.1010, 1 (2023)

    work page 2023

  15. [15]

    Schützhold, H

    R. Schützhold, H. Gies, and G. Dunne, Dynamically assisted Schwinger mechanism, Phys. Rev. Lett.101, 130404 (2008)

    work page 2008

  16. [16]

    Orthaber, F

    M. Orthaber, F. Hebenstreit, and R. Alkofer, Momentum spec- tra for dynamically assisted Schwinger pair production, Phys. Lett. B698, 80 (2011)

    work page 2011

  17. [17]

    Fey and R

    C. Fey and R. Schützhold, Momentum dependence in the dy- namically assisted Sauter-Schwinger effect, Phys. Rev. D85, 025004 (2012)

    work page 2012

  18. [18]

    Nuriman, B

    A. Nuriman, B. S. Xie, Z. L. Li, and D. Sayipjamal, Enhanced electron-positron pair creation by dynamically assisted combi- national fields, Phys. Lett. B717, 465 (2012)

    work page 2012

  19. [19]

    Kohlfürst, M

    C. Kohlfürst, M. Mitter, G. von Winckel, F. Hebenstreit, and R. Alkofer, Optimizing the pulse shape for Schwinger pair pro- duction, Phys. Rev. D88, 045028 (2013)

    work page 2013

  20. [20]

    I. Akal, S. Villalba-Chávez, and C. Müller, Electron-positron pair production in a bifrequent oscillating electric field, Phys. Rev. D90, 113004 (2014)

    work page 2014

  21. [21]

    Hebenstreit and F

    F. Hebenstreit and F. Fillion-Gourdeau, Optimization of Schwinger pair production in colliding laser pulses, Phys. Lett. B739, 189 (2014)

    work page 2014

  22. [22]

    M. F. Linder, C. Schneider, J. Sicking, N. Szpak, and R. Schützhold, Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect, Phys. Rev. D92, 085009 (2015)

    work page 2015

  23. [23]

    A. Otto, D. Seipt, D. Blaschke, B. Kämpfer, and S. A. Smolyan- sky, Assisted dynamical Schwinger effect: pair production in a pulsed bifrequent field, Phys. Lett. B740, 335 (2015)

    work page 2015

  24. [24]

    A. Otto, D. Seipt, D. Blaschke, S. A. Smolyansky, and B. Kämpfer, Assisted vacuum decay by time-dependent elec- tric fields, Phys. Rev. D91, 105018 (2015)

    work page 2015

  25. [25]

    I. A. Aleksandrov, G. Plunien, and V . M. Shabaev, Dynami- cally assisted Schwinger effect beyond the spatially-uniform- field approximation, Phys. Rev. D97, 116001 (2018)

    work page 2018

  26. [26]

    L. J. Li, M. Mohamedsedik, and B. S. Xie, Enhanced dynami- cally assisted pair production in spatial inhomogeneous electric fields with the frequency chirping, Phys. Rev. D104, 036015 (2021)

    work page 2021

  27. [27]

    Torgrimsson, C

    G. Torgrimsson, C. Schneider, and R. Schützhold, Dynami- cally assisted Sauter-Schwinger effect — non-perturbative ver- sus perturbative aspects, J. High Energy Phys. 06 (2017) 043

    work page 2017

  28. [28]

    Torgrimsson, Perturbative methods for assisted nonperturba- tive pair production, Phys

    G. Torgrimsson, Perturbative methods for assisted nonperturba- tive pair production, Phys. Rev. D99, 096002 (2019)

    work page 2019

  29. [29]

    G. V . Dunne, H. Gies, and R. Schützhold, Catalysis of Schwinger vacuum pair production, Phys. Rev. D80, 111301(R) (2009)

    work page 2009

  30. [30]

    Schneider and R

    C. Schneider and R. Schützhold, Dynamically assisted Sauter- Schwinger effect in inhomogeneous electric fields, J. High En- ergy Phys. 02 (2016) 164

    work page 2016

  31. [31]

    Taya, Dynamically assisted Schwinger mechanism and chi- rality production in parallel electromagnetic field, Phys

    H. Taya, Dynamically assisted Schwinger mechanism and chi- rality production in parallel electromagnetic field, Phys. Rev. Res.2, 023257 (2020)

    work page 2020

  32. [32]

    Kohlfürst, F

    C. Kohlfürst, F. Queisser, and R. Schützhold, Dynamically assisted tunneling in the impulse regime, Phys. Rev. Res.3, 033153 (2021)

    work page 2021

  33. [33]

    Y . Ren, C. Luo, and I. Sitiwaldi, Dynamically assisted Schwinger mechanism in spatially separated electric fields, Phys. Rev. A107, 012210 (2023)

    work page 2023

  34. [34]

    N. Z. Chen, O. Amat, L. N. Hu, H. H. Fan, and B. S. Xie, 13 Asymmetric pulse effects on pair production in chirped electric fields, Phys. Rev. D109, 076015 (2024)

    work page 2024

  35. [35]

    I. A. Aleksandrov, D. G. Sevostyanov, and V . M. Shabaev, Schwinger particle production: Rapid switch off of the external field versus dynamical assistance, Phys. Rev. D111, 016010 (2025)

    work page 2025

  36. [36]

    J. Braß, D. M. Müller, S. Villalba-Chávez, K. Krajewska, and C. Müller, Relative-phase dependence of dynamically assisted electron-positron pair creation in the superposition of strong os- cillating electric-field pulses, arXiv:2505.24488

    work page arXiv

  37. [37]

    Jangir and A

    A. Jangir and A. Ahmed, Carrier-envelope phase and pulse- shape effects on vacuum pair production in asymmetric electric fields with bell-shaped envelopes, Phys. Rev. D113, 096002 (2026)

    work page 2026

  38. [38]

    Wöllert, H

    A. Wöllert, H. Bauke, and C. H. Keitel, Spin polarized electron- positron pair production via elliptical polarized laser fields, Phys. Rev. D91, 125026 (2015)

    work page 2015

  39. [39]

    Blinne and E

    A. Blinne and E. Strobel, Comparison of semiclassical and Wigner function methods in pair production in rotating fields, Phys. Rev. D93, 025014 (2016)

    work page 2016

  40. [40]

    Z. L. Li, Y . J. Li, and B. S. Xie, Momentum vortices on pairs production by two counter-rotating fields, Phys. Rev. D96, 076010 (2017)

    work page 2017

  41. [41]

    X. G. Huang, M. Matsuo, and H. Taya, Spontaneous generation of spin current from the vacuum by strong electric fields, Prog. Theor. Exp. Phys.2019, 113B02 (2019)

    work page 2019

  42. [42]

    Olugh, Z

    O. Olugh, Z. L. Li, B. S. Xie, and R. Alkofer, Pair production in differently polarized electric fields with frequency chirps, Phys. Rev. D99, 036003 (2019)

    work page 2019

  43. [43]

    Kohlfürst, Spin states in multiphoton pair production for cir- cularly polarized light, Phys

    C. Kohlfürst, Spin states in multiphoton pair production for cir- cularly polarized light, Phys. Rev. D99, 096017 (2019)

    work page 2019

  44. [44]

    Z. L. Li, B. S. Xie, and Y . J. Li, Boson pair production in arbitrarily polarized electric fields, Phys. Rev. D100, 076018 (2019)

    work page 2019

  45. [45]

    Olugh, Z

    O. Olugh, Z. L. Li, and B. S. Xie, Dynamically assisted pair production for various polarizations, Phys. Lett. B802, 135259 (2020)

    work page 2020

  46. [46]

    L. N. Hu, O. Amat, L. Wang, A. Sawut, H. H. Fan, and B. S. Xie, Momentum spirals in multiphoton pair production revisited, Phys. Rev. D107, 116010 (2023)

    work page 2023

  47. [47]

    Yu, Evolution of chirality in a multiphoton pair production process, Phys

    C. Yu, Evolution of chirality in a multiphoton pair production process, Phys. Rev. D108, 116009 (2023)

    work page 2023

  48. [48]

    L. N. Hu, H. H. Fan, O. Amat, S. Tang, and B. S. Xie, Spin effect induced momentum spiral and asymmetry degree in pair production, Phys. Rev. D110, 056013 (2024)

    work page 2024

  49. [49]

    M. M. Majczak, K. Krajewska, J. Z. Kami ´nski, and A. Bech- ler, Scattering matrix approach to dynamical Sauter-Schwinger process: Spin- and helicity-resolved momentum distributions, Phys. Rev. D110, 116025 (2024)

    work page 2024

  50. [50]

    I. A. Aleksandrov and A. Kudlis, Pair production in rotating electric fields via quantum kinetic equations: Resolving helicity states, Phys. Rev. D110, L011901 (2024)

    work page 2024

  51. [51]

    R. Z. Jiang, Z. L. Li, and Y . J. Li, Study of spin states in vac- uum pair production via the Dirac-Heisenberg-Wigner formal- ism, arXiv:2510.00455

    work page arXiv

  52. [52]

    Kohlfürst, Pair production in circularly polarized waves, Phys

    C. Kohlfürst, Pair production in circularly polarized waves, Phys. Rev. D110, L111903 (2024)

    work page 2024

  53. [53]

    Z. Y . Chen, O. Amat, J. H. Bai, and M. A. Bake, Spin effect in vacuum pair production under two-color rotating electric fields, Phys. Rev. D111, 116005 (2025)

    work page 2025

  54. [54]

    M. A. Bake and O. Olugh, Vacuum pair production in spatially asymmetric time-oscillating electric fields, Phys. Rev. D112, 016030 (2025)

    work page 2025

  55. [55]

    I. A. Aleksandrov, A. Kudlis, and A. I. Klochai, Kinetic theory of vacuum pair production in uniform electric fields revisited, Phys. Rev. Res.6, 043009 (2024)

    work page 2024

  56. [56]

    V . N. Pervushin and V . V . Skokov, Kinetic description of fermion production in the oscillator representation, Acta Phys. Pol. B37, 2587 (2006)

    work page 2006

  57. [57]

    Z. L. Li, R. Z. Jiang, and Y . J. Li, Nonadiabatic quantum ki- netic equations and Dirac-Heisenberg-Wigner formalism for Schwinger pair production in time-varying electric fields with multiple components, arXiv:2503.02530

    work page arXiv

  58. [58]

    I. A. Aleksandrov, V . A. Bokhan, A. I. Baksheev, and A. Kudlis, Vacuum polarization and pair production in time- dependent electric fields: A quantum-kinetic-equation ap- proach, arXiv:2602.00873

    work page arXiv

  59. [59]

    A. G. Tkachev, I. A. Aleksandrov, and V . M. Shabaev, Schwinger pair production in counterpropagating laser pulses: Identifying volume factors, Phys. Rev. A111, 053121 (2025)

    work page 2025

  60. [60]

    Kohlfürst, H

    C. Kohlfürst, H. Gies, and R. Alkofer, Effective mass signatures in multiphoton pair production, Phys. Rev. Lett.112, 050402 (2014)

    work page 2014

  61. [61]

    I. A. Aleksandrov, G. Plunien, and V . M. Shabaev, Locally- constant field approximation in studies of electron-positron pair production in strong external fields, Phys. Rev. D99, 016020 (2019)

    work page 2019

  62. [62]

    D. G. Sevostyanov, I. A. Aleksandrov, G. Plunien, and V . M. Shabaev, Total yield of electron-positron pairs produced from vacuum in strong electromagnetic fields: Validity of the locally constant field approximation, Phys. Rev. D104, 076014 (2021)

    work page 2021

  63. [63]

    I. A. Aleksandrov, D. G. Sevostyanov, and V . M. Shabaev, Par- ticle production in strong electromagnetic fields and local ap- proximations, Symmetry14, 2444 (2022)

    work page 2022

  64. [64]

    Kluger, J

    Y . Kluger, J. M. Eisenberg, B. Svetitsky, F. Cooper, and E. Mot- tola, Fermion pair production in a strong electric field, Phys. Rev. D45, 4659 (1992)

    work page 1992

  65. [65]

    Blinne and H

    A. Blinne and H. Gies, Pair production in rotating electric fields, Phys. Rev. D89, 085001 (2014)

    work page 2014

  66. [66]

    I. A. Aleksandrov and C. Kohlfürst, Pair production in tempo- rally and spatially oscillating fields, Phys. Rev. D101, 096009 (2020)

    work page 2020

  67. [67]

    A. I. Nikishov, Pair production by a constant external field, Zh. Eksp. Teor. Fiz.57, 1210 (1969) [Sov. Phys. JETP30, 660 (1970)]

    work page 1969