Speaker
Description
The Schwinger effect is a nonperturbative manifestation of vacuum instability and cannot be captured by a finite-order expansion in the external electric field. Its standard treatment already involves an appropriate resummation. For example, the vacuum decay rate is obtained in the in-out formalism from the imaginary part of the one-loop effective action, which compactly represents the sum of relevant one-particle-irreducible contributions in the background field.
The situation is more subtle in the in-in formalism. One may naively expect that the pair-production effect can be incorporated by computing a one-loop effective action along the closed-time path. However, because the in-in formalism involves 2 x 2 matrix propagators, such a direct calculation is technically involved and less transparent. Moreover, the physical targets in the in-in formalism are real-time expectation values of operators, rather than the vacuum persistence amplitude itself. Therefore, the techniques used in the in-out formalism cannot simply be transplanted to the closed-time path, and an efficient resummation scheme suited for real-time observables is required.
In this talk, we present such a resummation scheme for a spatially homogeneous and time-independent electric field. The key step is to recast the boundary wavefunctions into quadratic self-energy-like terms in the functional integration formalism. The resulting generating functional in the modified in-in formalism leads to propagators that resum the infinite diagrams necessary to capture the vacuum-instability effects. With these modified propagators, real-time expectation values can be computed through ordinary one-loop diagrams while already incorporating the Schwinger pair-production effect.
As an application, we compute the in-in expectation value of the vector current and show that a simple one-loop calculation with the modified propagators captures the pair-production effect.
This talk is based on JHEP 05 (2026) 139.