Exact one-loop QED actions in global $\mathrm{(A)dS}_2$

TL;DR

This paper derives exact one-loop QED effective actions for spinor fields in uniform electric fields within global (A)dS$_2$ spacetime, revealing the interplay between electric fields and curvature and connecting to pair production phenomena.

Contribution

It provides the first exact expressions for one-loop QED actions in (A)dS$_2$, linking scattering matrices, Bogoliubov coefficients, and pair production in curved spacetime.

Findings

Effective actions expressed via proper-time integrals and Hurwitz zeta functions.

Reproduction of pure (A)dS$_2$ and Minkowski limits.

Insights into the interplay between electric fields and spacetime curvature.

Abstract

Using the in-out formalism, we derive the exact one-loop QED effective actions for spinor field in a uniform electric field in two-dimensional global (anti-)de Sitter (A)dS$_2$ spacetime. The one-loop effective action probed by a scalar or spinor field is determined by the scattering matrix relating the out-vacuum to the in-vacuum, which is in turn fixed by the Bogoliubov coefficients of the corresponding Klein-Gordon or Dirac equation in the presence of both a gauge field and curved spacetime. Remarkably, the vacuum persistence amplitude -- twice the imaginary part of the one-loop effective action -- is related, via the Bogoliubov relations, to the mean number of particle-antiparticle pairs spontaneously produced by the background fields. The Bogoliubov coefficients or mean number of pair-production for charged scalar and spinor fields in global (A)dS$_2$ lead to QED effective actions expressed in terms of both proper-time integrals and Hurwitz zeta functions. These effective actions reveal a strong interplay between the electric field and spacetime curvature and correctly reproduce the limiting cases of pure (A)dS$_2$ spacetime and a uniform electric field in Minkowski space. We further discuss the physical implications of the resulting QED effective actions in (A)dS$_2$.