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The Sauter-Schwinger effect, Schwinger effect or Schwinger pair production is a predicted physical phenomenon whereby matter is created by a strong electric field. It is a prediction of quantum electrodynamics (QED) in which electron-positron pairs are spontaneously created in the presence of an electric field, thereby causing the decay of the electric field. It was originally proposed by Fritz Sauter in 1931^[1] and further important work was carried out by Werner Heisenberg and Hans Heinrich Euler in 1936^[2], though it was not until 1951 when Julian Schwinger gave a complete theoretical description ^[3].

The Schwinger effect has never been observed due to the extremely strong electric-field strengths required. Pair production takes place exponentially slowly when the electric field strength is significantly below the Schwinger limit, corresponding to approximately $\times 10^{18}\,\mathrm {V} /\mathrm {m}$ . The rate of pair production may be significantly increased in time-dependent electric fields ^[4]^[5]^[6], and as such is being pursued by high-intensity laser experiments ^[7].

Mathematical description

The Schwinger effect in a constant electric field takes place at a constant rate per unit volume, commonly referred to as $\Gamma$ . The rate was first calculated by Schwinger^[3] and is equal to

\Gamma ={\frac {(eE)^{2}}{4\pi ^{3}}}\mathrm {e} ^{-\pi m^{2}/eE}

where $e$ is the (magnitude of the) charge of an electron, $m$ is the mass of an electron and $E$ is the electric field strength. This formula cannot be expanded in a Taylor series in $e^{2}$ , showing the nonperturbative nature of this effect.

References

^ F. Sauter, "Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs", Zeitschrift für Physik, 82 (1931) pp. 742–764. doi:10.1007/BF01339461
^ W. Heisenberg and H. Euler, "Folgerungen aus der Diracschen Theorie des Positrons", Zeitschrift für Physik, 98 (1936) pp. 714-732. doi:10.1007/BF01343663 English translation
^ ^a ^b J. Schwinger, "On Gauge Invariance and Vacuum Polarization", Phys. Rev.,82 (1951) pp. 664–679. doi:10.1103/PhysRev.82.664
^ Brezin, E., and C. Itzykson. "Pair production in vacuum by an alternating field." Physical Review D 2(7) (1970) 1191
^ Ringwald, Andreas. "Pair production from vacuum at the focus of an X-ray free electron laser." Physics Letters B 510.1-4 (2001): 107-116.doi:10.1016/S0370-2693(01)00496-8
^ Popov, Vladimir Stepanovich. "Schwinger mechanism of electron-positron pair production by the field of optical and X-ray lasers in vacuum." Journal of Experimental and Theoretical Physics Letters 74.3 (2001): 133-138.doi:10.1134/1.1410216
^ I. C. E. Turcu et al., "High field physics and QED experiments at ELI-NP", Rom. Rep. Phys., 68, S145 (2016).

[1] F. Sauter, "Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs", Zeitschrift für Physik, 82 (1931) pp. 742–764. doi:10.1007/BF01339461

[2] W. Heisenberg and H. Euler, "Folgerungen aus der Diracschen Theorie des Positrons", Zeitschrift für Physik, 98 (1936) pp. 714-732. doi:10.1007/BF01343663 English translation

[Schwinger-3] J. Schwinger, "On Gauge Invariance and Vacuum Polarization", Phys. Rev.,82 (1951) pp. 664–679. doi:10.1103/PhysRev.82.664

[4] Brezin, E., and C. Itzykson. "Pair production in vacuum by an alternating field." Physical Review D 2(7) (1970) 1191

[5] Ringwald, Andreas. "Pair production from vacuum at the focus of an X-ray free electron laser." Physics Letters B 510.1-4 (2001): 107-116.doi:10.1016/S0370-2693(01)00496-8

[6] Popov, Vladimir Stepanovich. "Schwinger mechanism of electron-positron pair production by the field of optical and X-ray lasers in vacuum." Journal of Experimental and Theoretical Physics Letters 74.3 (2001): 133-138.doi:10.1134/1.1410216

[7] I. C. E. Turcu et al., "High field physics and QED experiments at ELI-NP", Rom. Rep. Phys., 68, S145 (2016).

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+The '''Sauter-Schwinger effect''', '''Schwinger effect''' or '''Schwinger pair production''' is a predicted physical phenomenon whereby matter is created by a strong electric field. It is a prediction of [[quantum electrodynamics]] (QED) in which electron-positron pairs are spontaneously created in the presence of an electric field, thereby causing the decay of the electric field. It was originally proposed by [[Fritz Sauter]] in 1931<ref>F. Sauter, "Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs", ''Zeitschrift für Physik'', '''82''' (1931) pp. 742–764. {{doi|10.1007/BF01339461}}</ref> and further important work was carried out by [[Werner Heisenberg]] and [[Hans Heinrich Euler]] in 1936<ref>W. Heisenberg and H. Euler, "Folgerungen aus der Diracschen Theorie des Positrons", ''Zeitschrift für Physik'', '''98''' (1936) pp. 714-732. {{doi|10.1007/BF01343663}} [https://arxiv.org/abs/physics/0605038 English translation]</ref>, though it was not until 1951 when [[Julian Schwinger]] gave a complete theoretical description <ref name="Schwinger">J. Schwinger, "On Gauge Invariance and Vacuum Polarization", ''Phys. Rev.'','''82''' (1951) pp. 664–679. {{doi|10.1103/PhysRev.82.664}}</ref>.
-#REDIRECT [[Schwinger limit]]
+The Schwinger effect has never been observed due to the extremely strong electric-field strengths required. Pair production takes place exponentially slowly when the electric field strength is significantly below the [[Schwinger limit]], corresponding to approximately <math>\times 10^{18} \, \mathrm{V} / \mathrm{m}</math>. The rate of pair production may be significantly increased in time-dependent electric fields <ref>Brezin, E., and C. Itzykson. "Pair production in vacuum by an alternating field." ''Physical Review D'' '''2(7)''' (1970) 1191</ref><ref>Ringwald, Andreas. "Pair production from vacuum at the focus of an X-ray free electron laser." ''Physics Letters B'' '''510.1-4''' (2001): 107-116.{{doi|10.1016/S0370-2693(01)00496-8}}</ref><ref>Popov, Vladimir Stepanovich. "Schwinger mechanism of electron-positron pair production by the field of optical and X-ray lasers in vacuum." ''Journal of Experimental and Theoretical Physics Letters'' '''74.3''' (2001): 133-138.{{doi|10.1134/1.1410216}}</ref>, and as such is being pursued by high-intensity laser experiments <ref>I. C. E. Turcu et al., "High field physics and QED experiments at ELI-NP", ''Rom. Rep. Phys.'', '''68''', S145 (2016).</ref>.
+==Mathematical description==
+The Schwinger effect in a constant electric field takes place at a constant rate per unit volume, commonly referred to as <math>\Gamma</math>. The rate was first calculated by Schwinger<ref name="Schwinger">J. Schwinger, "On Gauge Invariance and Vacuum Polarization", ''Phys. Rev.'','''82''' (1951) pp. 664–679. {{doi|10.1103/PhysRev.82.664}}</ref> and is equal to
+:<math> \Gamma = \frac{ (e E)^2 }{ 4 \pi^3} \mathrm{e}^{-\pi m^2/eE} </math>
+where <math>e</math> is the (magnitude of the) charge of an electron, <math>m</math> is the mass of an electron and <math>E</math> is the electric field strength. This formula cannot be expanded in a Taylor series in <math>e^2</math>, showing the nonperturbative nature of this effect.
+==See also==
+*[[Julian Schwinger]]
+*[[Schwinger limit]]
+*[[Vacuum polarization]]
+==References==
+<references />
+[[Category:Particle physics]]
+[[Category:Hypothetical processes]]
+[[Category:Quantum electrodynamics]]