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arXiv · hep-th/0602176

Worldline Instantons II: The Fluctuation Prefactor

Gerald V. Dunne·Holger Gies·Christian Schubert·Qing-hai Wang
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Abstract

In a previous paper [1], it was shown that the worldline expression for the nonperturbative imaginary part of the QED effective action can be approximated by the contribution of a special closed classical path in Euclidean spacetime, known as a worldline instanton. Here we extend this formalism to compute also the prefactor arising from quantum fluctuations about this classical closed path. We present a direct numerical approach for determining this prefactor, and we find a simple explicit formula for the prefactor in the cases where the inhomogeneous electric field is a function of just one spacetime coordinate. We find excellent agreement between our semiclassical approximation, conventional WKB, and recent numerical results using numerical worldline loops.

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Gerald V. Dunne, Holger Gies, Christian Schubert, Qing-hai Wang. 2006-03-30. Worldline Instantons II: The Fluctuation Prefactor. https://doi.org/10.1103/physrevd.73.065028

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