Thimble regularization is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the fact that one in general needs to collect contributions coming from more than one thimble. Here we explore the idea of performing Taylor expansions on Lefschetz thimbles. We show that in some cases we can compute expansions in regions where only the dominant thimble contributes to the result in such a way that these (different, disjoint) regions can be bridged. This can most effectively be done via Padé approximants. In this way multi-thimble simulations can be circumvented. The approach can be trusted provided we can show that the analytic continuation we are performing is a legitimate one, which thing we can indeed show. We briefly discuss two prototypal computations, for which we obtained a very good control on the analytical structure (and singularities) of the results. All in all, the main strategy that we adopt is supposed to be valuable not only in the thimble approach, which thing we finally discuss.

中文翻译：

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在Lefschetz顶针上的Taylor展开

顶针正则化是符号问题的一种可能解决方案，该问题可以通过在作用的虚部保持恒定的流形（Lefschetz顶针）上建立量子场理论来规避。一个主要的障碍是由于这样一个事实，一个人通常需要收集来自多个顶针的捐款。在这里，我们探讨在Lefschetz顶针上执行泰勒展开的想法。我们表明，在某些情况下，我们可以计算仅占主导地位的顶针对结果有贡献的区域中的扩展，从而可以桥接这些（不同，不相交）的区域。这可以通过Padé近似值最有效地完成。这样，可以避免多套管模拟。只要我们可以证明我们执行的分析连续性是合法的，该方法就可以被信任，我们确实可以展示的东西。我们简要讨论了两个原型计算，对于它们，我们对结果的分析结构（和奇点）获得了很好的控制。总而言之，我们采用的主要策略不仅在顶针方法中很有价值，而且我们将最终讨论。