Recently, Gies and Karbstein showed that the two-loop Euler-HeisenbergLagrangian receives a finite one-particle reducible contribution in addition tothe well-known one-particle irreducible one. Here, we demonstrate that asimilar contribution exists for the propagator in a constant field already atthe one-loop level, and we calculate this contribution for the scalar QED case.We also present an independent derivation of the Gies-Karbstein result usingthe worldline formalism, treating the scalar and spinor QED cases in a unifiedmanner.
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机译：最近，吉斯和卡尔布施泰因（Gies and Karbstein）表明，除了众所周知的单粒子不可约性之外，二环Euler-HeisenbergLagrangian还获得了有限的一粒子可约性贡献。在这里，我们证明了已经在单循环水平的恒定场中传播子存在类似的贡献，并且我们针对标量QED情况计算了该贡献。标量和旋量QED案例采用统一方式。
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