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

Yutaro Shoji

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arXiv · 2605.07934

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

Yutaro Shoji

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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.

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Yutaro Shoji. 2026-05-08. Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis. https://arxiv.org/abs/2605.07934

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