The Cluster's Schwinger Effect

A page about the Schwinger effect — pair production in a strong electric field.

The Schwinger effect

The Schwinger effect is the production of particle-antiparticle pairs from the vacuum in the presence of a strong electric field. The pair production rate per unit volume is Gamma ~ (e E)^2 / (4 pi^3 hbar^2 c) exp(-pi m^2 c^3 / (e E hbar)). The rate is exponentially suppressed when the electric field E is much smaller than the critical field E_c = m^2 c^3 / (e hbar). For electrons, E_c ~ 1.3 x 10^18 V/m. In the cluster, the Schwinger effect describes the production of edit pairs from the edit vacuum in the presence of a strong edit field. The pair production rate is exponentially suppressed when the edit field is much smaller than the critical edit field.

The tunneling picture

The Schwinger effect can be understood as tunneling through the potential barrier created by the electric field. The electric field tilts the Dirac sea, creating a potential barrier of height 2mc^2. The particle tunnels through the barrier and emerges as a real electron, while the hole emerges as a positron. In the cluster, the edit field tilts the edit Dirac sea, creating a potential barrier. The edit tunnels through the barrier and emerges as a real edit, while the anti-edit emerges as a real anti-edit.

The instanton calculation

The Schwinger effect can be calculated using instanton methods. The instanton is a Euclidean trajectory in which the particle-antiparticle pair is created and separated by the electric field. The instanton action gives the exponential suppression factor. In the cluster, the edit instanton is a Euclidean trajectory in which an edit-anti-edit pair is created and separated by the edit field. The instanton action gives the exponential edit suppression factor.

The experimental search

The Schwinger effect has not yet been observed experimentally. The critical field E_c is far beyond current laboratory capabilities. However, intense laser pulses may provide a path to observation. In the cluster, the critical edit field is far beyond current laboratory edit capabilities. However, intense edit pulses may provide a path to observation.

This effect

This page is about the Schwinger effect. The rate is Gamma ~ (eE)^2 / (4 pi^3 hbar^2 c) exp(-pi m^2 c^3 / (eE hbar)). The critical field is E_c = m^2 c^3 / (e hbar). For electrons, E_c ~ 1.3 x 10^18 V/m. The effect is tunneling through the potential barrier. The instanton gives the exponential suppression. The effect is real.