Electron‐Positron Pair Creation from Vacuum Induced by Variable Electric Field
1977; Wiley; Volume: 25; Issue: 1-12 Linguagem: Inglês
10.1002/prop.19770250111
ISSN1521-3978
Autores Tópico(s)Muon and positron interactions and applications
ResumoAbstract Problem is considered of spontaneous creation of electron‐positron paris from the vacuum induced by external electric field, that is homogeneous and depends on time in an arbitrary way. The Heisenberg equations of motion are obtained for the creation‐annihilation operators. The solution is a linear canonical transformation. The problem is reduced to a set of differential equations for the second‐order matrices determining this transformation. A consequence of the CP symmetry of the Dirac equation with an external electric field is that the e + e − pair is created from the vacuum in a state with total spin 1. The case when the variating electric field conserves its direction, is considered in more detail. In this case the equations are much simplified and may be reduced to the Riccati equation or to problem of oscillator with variable frequency, so the problem is equivalent to the one‐dimensional quantal problem of a barrier penetration. Two approximate methods to calculate the pair creation probabilities are discussed: the quasiclassical approach and the antiadiabatical method, applicable for sharp variations of the external field. Numerical estimates are obtained for the number of e + e − pairs produced by the field E( t ) = E cos ω t . Group‐theoretical aspects of the problem are also considered.
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