Crossing singularities in the saddle point approximation

• URL: http://arxiv.org/abs/2309.12427v1
• Date: Thu, 21 Sep 2023 18:50:12 GMT
• Title: Crossing singularities in the saddle point approximation
• Authors: Job Feldbrugge, Dylan L. Jow, and Ue-Li Pen
• Abstract summary: We show that complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value problem. These analytically continued complex paths enrich the study of real-time Feynman path integrals.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value problem. We show that the behavior is universal and central to the problem of quantum tunneling. These analytically continued complex classical paths enrich the study of real-time Feynman path integrals.

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