New partial resummation of the QED effective action

Abstract

We explain a conjecture which states that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be partially summed in all terms containing the field-strength invariants $\mathcal{F}=\frac{1}{4}{F}_{\mu \nu }{F}^{\mu \nu }(x)$, $\mathcal{G}=\frac{1}{4}{\tilde{F}}_{\mu \nu }{F}^{\mu \nu }(x)$. This summation is encapsulated in a factor with the same form as the (spacetime-dependent) Heisenberg-Euler Lagrangian density. We also discuss some implications and a possible extension in presence of gravity. We will focus on the scalar field case.

Comments: 10 pages. Contribution to the Marcel Grossmann Meeting 2021