![[PukiWiki]](image/pukiwiki.png "[PukiWiki]")
Title: Apperance of fixed singularities and modified normalization in the Borel-summed WKB method †Speaker: Ryo Namba †The Borel sum applied to the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) method, often called exact WKB, is a powerful tool for a systematic treatment of Schrodinger-type second-order differential equations and gives a mathematical interpretation of particle production in physics as the crossing of Stokes curves, as Koki Tokeshi showed at the RESCEU seminar on Nov. 14. However, interestingly, caution is needed in the cases where multiple turning points of a differential equation are connected by Stokes curves. This is due to the fact that a new type of singularities, called "fixed singularities", appear in the Borel-transformed space. A careful analysis can show that these singularities do not make the final result divergent but do change the asymptotic behavior of the Borel-summed solution. In this talk, I will show that the exact WKB method can reproduce the result of Koffman-Linde Starobinsky 1997 only after taking into account this modification. |