1998/07/31 by Gerald V. Dunne, Gerald Dunne, Theodore Hall · 1 voice · 106 citations
Engineering · Mathematics · Physics and Astronomy · #Action (physics) #Algorithm #Black Holes and Theoretical Physics #Classical mechanics #Computation #Computer science #Constant (computer programming) #Dispersion relation #Effective action #Electric field #Expression (computer science) #Magnetic field #Mathematical analysis #Mathematics #Particle Accelerators and Free-Electron Lasers #Physics #Pulsars and Gravitational Waves Research #Quantum electrodynamics #Quantum mechanics #Resolvent #Semiclassical physics #Statistical physics #WKB approximation #hep-th
paper · pdf · doi:10.1103/physrevd.58.105022
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 58(10) (American Physical Society) · 27 pages, no figures; reference added
arxiv created 1998/08/12 · openalex publication_date 1998/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We apply the resolvent technique to the computation of the QED effective action in time dependent electric field backgrounds. The effective action has both real and imaginary parts, and the imaginary part is related to the pair production probability in such a background. The resolvent technique has been applied previously to spatially inhomogeneous magnetic backgrounds, for which the effective action is real. We explain how dispersion relations connect these two cases, the magnetic case which is essentially perturbative in nature, and the electric case where the imaginary part is nonperturbative. Finally, we use a uniform semiclassical approximation to find an expression for very general time dependence for the background field. This expression is remarkably similar in form to Schwinger's classic result for the constant electric background.