论文标题
泰勒（Taylor
Taylor expansions on Lefschetz thimbles (and not only that)
论文作者
论文摘要
顶针正则化是对符号问题的可能解决方案，该解决方案是通过在动作中假想部分保持恒定（lefschetz thimbles）上的歧管上的量子场理论来避免的。一个主要的障碍是因为总体上需要收集来自多个顶针的捐款。在这里，我们探讨了在Lefschetz Thimbles上进行泰勒扩展的想法。我们表明，在某些情况下，我们可以计算只有主要顶针有助于结果的区域的扩张，以使这些（不同的，不相交的区域）可以桥接。这可以通过Padé近似值来完成。以这种方式，可以规避多层化模拟。只要我们可以证明我们正在执行的分析延续是合法的，我们确实可以表现出来，就可以信任该方法。我们简要讨论了两个原型计算，为此我们对结果的分析结构（和奇异性）进行了很好的控制。总而言之，我们采用的主要策略不仅在顶针方法中是有价值的，而且我们终于讨论哪件事。
Thimble regularisation 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.
