Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis

High Energy Physics - Theory [Submitted on 8 May 2026 (v1), last revised 1 Jun 2026 (this version, v2)] Title:Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis View PDF HTML (experimental)Abstract:We present a comprehensive Lefschetz thimble analysis of the one-dimensional Salpeter equation under a strong electric field. By treating the non-local square-root operator within the framework of algebraic analysis, we construct the full solution space, which includes relativistic generalizations of the Airy Ai and Bi functions and their negative-energy counterparts. Through a direct comparison with the Dirac and Klein-Gordon equations, we provide a geometric explanation for the absence of Klein paradox and the Schwinger effect in the Salpeter equation. Furthermore, our findings establish a unified geometric interpretation of the Schwinger effect across different relativistic wave equations. Submission history From: Yutaro Shoji [view email][v1] Fri, 8 May 2026 16:05:23 UTC (3,028 KB) [v2] Mon, 1 Jun 2026 17:09:03 UTC (3,268 KB) Current browse context: hep-th References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.