$(\mathcal{F},\mathcal{G})$ -QED有效action的求和形式
$(\mathcal{F},\mathcal{G})$-summed form of the QED effective action
摘要：
我们猜想，量子电动力学的单圈有效拉格朗日量的适当的时间序列展开，可以在所有的条款，包含场强不变量$\mathcal{F} = \frac{1}{4} F_{μν}F^{μν} (x)$，$\mathcal{G}= \frac{1}{4} \tilde F_{μν}F^{μν}(x)$，包括那些也拥有电磁场强度的导数求和。这个部分的重新计算被精确地封装在一个因子中，这个因子的形式与海森堡-欧拉拉格朗日密度的形式相同，只是现在电场和磁场可以任意依赖于时空坐标。我们为这个猜想提供了强有力的证据，并在适当的时候得到了六阶证明。此外，作为副产品，我们产生了一些可解的电磁背景。我们还讨论了广义的施温格公式的非恒定电场诱导的对生产的影响。最后，我们简要地概述了这些结果在引力存在下的扩展。
英文摘要：
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants $\mathcal{F} = \frac{1}{4} F_{μν}F^{μν} (x)$, $\mathcal{G}= \frac{1}{4} \tilde F_{μν}F^{μν}(x)$, including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity.
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