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Two-loop self-dual Euler-Heisenberg Lagrangians (II): Imaginary part and Borel analysis

Gerald V. Dunne·Christian Schubert
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Abstract

We analyze the structure of the imaginary part of the two-loop Euler-Heisenberg QED effective Lagrangian for a constant self-dual background. The novel feature of the two-loop result, compared to one-loop, is that the prefactor of each exponential (instanton) term in the imaginary part has itself an asymptotic expansion. We also perform a high-precision test of Borel summation techniques applied to the weak-field expansion, and find that the Borel dispersion relations reproduce the full prefactor of the leading imaginary contribution.

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Gerald V. Dunne, Christian Schubert. 2002-09-09. Two-loop self-dual Euler-Heisenberg Lagrangians (II): Imaginary part and Borel analysis. https://doi.org/10.1088/1126-6708%2F2002%2F06%2F042

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