AI 中文总结
研究球对称时空中大量粒子的径向作用，通过计算沿类双曲线测地线的径向作用，利用特殊函数展示重整性质，推广零测地线结果，还在4维史瓦西黑洞时空情形下关联量子a - 圈与径向作用，给出相关重整表达式及对偶a_D - 圈展开式。
AI 中文摘要
我们计算了各种球对称时空中沿类双曲线测地线的大量粒子的径向作用：标准的4维史瓦西时空、其d维推广即史瓦西 - 唐赫里尼解以及D3 - 膜时空，在eikonal极限下展示了关于特殊（超几何、福克斯 - 赖特）函数的有用重整性质并推广了之前对零测地线有效的结果。由此散射角也能被重整，我们明确展示了重整后的表达式。此外，在4维史瓦西黑洞时空这一更有趣的情形中，遵循量子塞伯格 - 维滕曲线处理与大量标量场相关的径向方程的方法，我们表明在这种大量情形下量子a - 圈（或等效地，“重整化角动量”）也与径向作用简单相关，给出了完全重整的表达式。最后，我们展示了对偶a_D - 圈的显式展开形式表达式，然而尚未得到其重整表达式。
英文摘要
We compute the massive particles radial action along hyperboliclike geodesics in various spherically symmetric spacetimes: the standard $4d$ Schwarzschild spacetime, its $d$-dimensional genralization known as Schwarzschild-Tangherlini solutions and for the D3-branes spacetimes, showing useful resummation properties in terms of special (hypergeometric, Fox-Wright) functions in the eikonal limit and generalizing previous results valid for null geodesics. As a consequence, the scattering angle can be resummed too, and we explicitly display the resummed expressions. In addition, in the more interesting situation of a $4d$ Schwarzschild black hole spacetime, following the approach of the quantum Seiberg-Witten curves to the radial equation associated with a massive scalar field, we show that the quantum $a$-cycle (or, equivalently, the \lq\lq renormalized angular momentum") is simply related to radial action also in this massive case, providing fully resummed expressions. Finally, we display the explicit, expanded-form expression of the dual $a_D$-cycle, for which, however, no resummed expressions have been derived yet.
Comments23 pages, no figures
