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Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity
High Energy Physics - Theory · Submitted 11 Nov 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting.
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The pair production of scalar particles in electromagnetic background fields is analyzed using real proper time formulation of 1-loop effective action. After explaining how real proper time formulation keeps unitarity of the particle creation process in an unambiguous way and discussing the (lack of) pair production in uniform (magnetic) electric backgrounds, we apply these ideas to general electric field backgrounds. Our approach is based on a recursive perturbative expansion of the proper time propagator $U(t)$ and we show how the pair production probabilities can be obtained from its singularities which arises upon a Pade summation of the expansion. We computed the pair production probabilities for general space or time dependent electric fields in locally constant approximation and showed they match with the well-known worldline instanton calculations of pulse and periodic backgrounds. Later, for one dimensional periodic electric and magnetic backgrounds, we showed how the WKB integrals appear in the classical limit. We linked both cases to specific WKB cycles in different spectral regions of the WKB problem and computed the WKB actions by evaluating the WKB integrals as well as by taking phase space integrals directly along Lefschetz thimbles. Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The pair production of scalar particles in electromagnetic background fields is analyzed using real proper time formulation of 1-loop effective action. | contribution 0.62 | 0.85 | 0.05 | asserted 0.99 |
| s1 | After explaining how real proper time formulation keeps unitarity of the particle creation process in an unambiguous way and discussing the (lack of) pair production in uniform (magnetic) electric backgrounds, we apply these ideas to general electric field backgrounds. | contribution 0.63 | 0.72 | 0.14 | asserted 0.91 |
| s2 | Our approach is based on a recursive perturbative expansion of the proper time propagator $U(t)$ and we show how the pair production probabilities can be obtained from its singularities which arises upon a Pade summation of the expansion. | method 0.99 | 0.93 | 0.17 | asserted 1.00 |
| s3 | We computed the pair production probabilities for general space or time dependent electric fields in locally constant approximation and showed they match with the well-known worldline instanton calculations of pulse and periodic backgrounds. | result 0.95 | 0.95 | 0.25 | asserted 1.00 |
| s4 | Later, for one dimensional periodic electric and magnetic backgrounds, we showed how the WKB integrals appear in the classical limit. | result 0.67 | 0.94 | 0.07 | asserted 1.00 |
| s5 | We linked both cases to specific WKB cycles in different spectral regions of the WKB problem and computed the WKB actions by evaluating the WKB integrals as well as by taking phase space integrals directly along Lefschetz thimbles. | contribution 0.58 | 0.94 | 0.13 | asserted 1.00 |
| s6 | Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting. | interpretation 0.44 | 0.92 | 0.38 | asserted 1.00 |
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The paper
Original abstract
The pair production of scalar particles in electromagnetic background fields is analyzed using real proper time formulation of 1-loop effective action. After explaining how real proper time formulation keeps unitarity of the particle creation process in an unambiguous way and discussing the (lack of) pair production in uniform (magnetic) electric backgrounds, we apply these ideas to general electric field backgrounds. Our approach is based on a recursive perturbative expansion of the proper time propagator $U(t)$ and we show how the pair production probabilities can be obtained from its singularities which arises upon a Pade summation of the expansion. We computed the pair production probabilities for general space or time dependent electric fields in locally constant approximation and showed they match with the well-known worldline instanton calculations of pulse and periodic backgrounds. Later, for one dimensional periodic electric and magnetic backgrounds, we showed how the WKB integrals appear in the classical limit. We linked both cases to specific WKB cycles in different spectral regions of the WKB problem and computed the WKB actions by evaluating the WKB integrals as well as by taking phase space integrals directly along Lefschetz thimbles. Finally, we explain the equivalence of our construction with exact WKB method in the classical limit by showing how the WKB cycles precisely contribute to the pair production process which is in complete agreement with our time dependent setting.
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What it cites · 44 sentences without a confident label
Uses the method or tool of 6 papers
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We first consider time dependent electric fields for [equation] As we stated above, this is effectively a one-dimensional problem and in principle it can be handled by exact WKB methods as in [ref] .
Exact WKB analysis of the vacuum pair production by time-dependent electric fields · Time Dependent Electric Fields: · 0.91
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The non-perturbative information is encoded in this divergent series and can be extracted using Borel-Pade techniques [ref] .
Schwinger pair production from Pad\'e-Borel reconstruction · Unambiguous Pair Production from Perturbative Expansions · 0.95
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The non-perturbative information is encoded in this divergent series and can be extracted using Borel-Pade techniques [ref] .
Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I · Unambiguous Pair Production from Perturbative Expansions · 0.95
Compares with 4 papers
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In this line of the paper, we first observed that the pair production probability arising from the analytical structure of $U^±(t)$ matches with the WLI calculations in [ref] .
Worldline Instantons II: The Fluctuation Prefactor · Introduction · 0.99
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In this line of the paper, we first observed that the pair production probability arising from the analytical structure of $U^±(t)$ matches with the WLI calculations in [ref] .
Worldline Instantons and Pair Production in Inhomogeneous Fields · Introduction · 0.99
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To a great extent, our results matched with [ref] where the authors generalized Schwinger's approach to non-uniform electromagnetic fields.
Derivative Expansion for the One-Loop Effective Lagrangian in QED · Introduction · 0.99
Cites as support 1 paper
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See [ref] for an example at 2 loops.] and the Borel integral have the same form. * When the proper time is chosen real, possible analytical continuation directions of the integral are defined by construction.
On the Higher Loop Euler-Heisenberg Trans-Series Structure · Introduction · 0.98
Cites as background 18 papers
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On the time dependent electric field side, the EWKB approach was recently discussed in [ref] where the particle creation was associated to the connection matrices between different Stokes regions.
Exact WKB analysis of the vacuum pair production by time-dependent electric fields · Connection to Exact WKB · 0.87
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In the presence of electric field backgrounds, they are widely used in computations of the pair production probabilities, which presents itself as the imaginary part of the effective action [ref] .
Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields · Introduction · 0.91
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In the presence of electric field backgrounds, they are widely used in computations of the pair production probabilities, which presents itself as the imaginary part of the effective action [ref] .
Worldline Instantons and Pair Production in Inhomogeneous Fields · Introduction · 0.91
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