Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917554717458432 |
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| author | Shoji, Yutaro |
| author_facet | Shoji, Yutaro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07934 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis Shoji, Yutaro High Energy Physics - Theory Mathematical Physics 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. |
| title | Topological Blocking of the Schwinger Effect in the Salpeter Equation: A Lefschetz Thimble Analysis |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2605.07934 |