On Adiabatic Pair Creation

  • Peter Pickl
  • Detlef Dürr


We give here a rigorous proof of the well known prediction of pair creation as it arises from the Dirac equation with an external time dependent potential. Pair creation happens with probability one if the potential changes adiabatically in time and becomes overcritical, which means that an eigenvalue curve (as a function of time) bridges the gap between the negative and positive spectral continuum. The potential can be thought of as being zero at large negative and large positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Süßmann [1] in 1963 and Gershtein and Zeldovich [8] in 1970.


Dirac Equation Dirac Operator Pair Creation Spectral Edge Stationary Phase Method 
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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria
  2. 2.Mathematisches Institut der Universität MünchenMünchenGermany

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