## Abstract

The initial-value problem for the quantum back reaction in spinor QED is formulated and solved in the semiclassical mean-field approximation for a homogeneous but time-dependent electric field E(t). We apply the method of adiabatic regularization to the Dirac equation in order to renormalize the expectation value of the current and derive a finite coupled set of ordinary differential equations for the time evolution of the system. We solve this system in 1+1 dimensions numerically and compare the solution to a simple model based on a relativistic Boltzmann-Vlasov equation, with a particle production source term inferred from the Schwinger particle creation rate and a Pauliblocking factor. This model reproduces very well the time behavior of the electric field and the creation rate of e+e- pairs of the semiclassical calculation.

Original language | English |
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Pages (from-to) | 4659-4671 |

Number of pages | 13 |

Journal | Physical Review D |

Volume | 45 |

Issue number | 12 |

DOIs | |

State | Published - 1992 |