Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-08
Phys.Rev.D75:045013,2007
Physics
High Energy Physics
High Energy Physics - Theory
RevTex, 12 pages, two figures; replaced by the version accepted in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.75.045013
Reformulating the instantons in a complex plane for tunneling or transmitting states, we calculate the pair-production rate of charged fermions in a spatially localized electric field, illustrated by the Sauter electric field E_0 sech^2 (z/L), and in a temporally localized electric field such as E_0 sech^2 (t/T). The integration of the quadratic part of WKB instanton actions over the frequency and transverse momentum leads to the pair-production rate obtained by the worldline instanton method, including the prefactor, of Phys. Rev. D72, 105004 (2005) and D73, 065028 (2006). It is further shown that the WKB instanton action plus the next-to-leading order contribution in spinor QED equals the WKB instanton action in scalar QED, thus justifying why the WKB instanton in scalar QED can work for the pair production of fermions. Finally we obtain the pair-production rate in a spatially localized electric field together with a constant magnetic field in the same direction.
Kim Sang Pyo
Page Don N.
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