Schwinger limit

The Schwinger limit is a limit value in quantum electrodynamics  (QED) from which non-linear effects for the electric field strength are expected. The only scale in QED is the mass of the electron . The oscillator limit is therefore comparable to the critical field ${\displaystyle m_{\mathrm {e} }}$

${\displaystyle E_{\mathrm {S} }={\frac {m_{\mathrm {e} }^{2}c^{3}}{e\hbar }}\approx 1{,}3\cdot 10^{18}{\rm {\frac {V}{m}}}}$

With

• the speed of light ${\displaystyle c}$
• the elementary charge ${\displaystyle e}$
• the reduced quantum of action . ${\displaystyle \hbar }$

Julian Schwinger showed in a fundamental essay from 1951 that at such field strengths the QED vacuum is unstable and decays due to the generation of electron- positron pairs. Schwinger calculated the effective QED Lagrange density for a constant external field and in a single-loop approximation. This has the imaginary part ${\displaystyle {\mathcal {L}}_{\mathrm {eff} }}$

${\displaystyle \Im {\mathcal {L}}_{\mathrm {eff} }={\frac {e^{2}E^{2}}{4\pi ^{3}}}\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}\exp \left\{-n\pi {\frac {m_{\mathrm {e} }^{2}}{eE}}\right\}}$

It determines the transition to another vacuum. ${\displaystyle \left|\langle {\mathit {Vac}}|{\mathit {Vac}}'\rangle \right|^{2}=\left|\exp(-\mathrm {i} {\mathcal {L}}_{\mathrm {eff} })\right|^{2}=\exp \left(2\Im {\mathcal {L}}_{\mathrm {eff} }\right)}$

Until 2014, lasers were n't powerful enough to achieve these field strengths, but future lasers may be able to do so.

literature

J. Schwinger: On Gauge Invariance and Vacuum Polarization , Physical Review 82, 664

Individual evidence

1. ↑ Bulanov et al .: On the Schwinger limit attainability with extreme power lasers . November 5, 2010, arxiv : 1007.4306 (English).