论文标题
基于Darboux和Puiseux定理的光谱重建和算法的重建
Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
论文作者
论文摘要
假设仅在某些量子场理论中，仅在Meromoromormormorthic两点函数（在固定波形处的复杂频率平面中）中单个模式的已知分散关系，我们研究了物理激发的完整频谱的何时以及如何重建。特别是，我们根据Darboux和Puiseux的定理开发了一种建设性算法，该算法允许对通过级别交叉连接的所有模式进行这种重建。为了具体，我们专注于已知模式是由流体动力梯度扩展描述的无间隙激发的理论，至少以某些（最好是高）已知。我们首先将算法应用于一个简单的代数示例，然后将算法应用于全息理论中的横向动量激发，该理论描述了一堆M2麸皮，并将动量扩散作为其无间隙的激发。
Assuming only a known dispersion relation of a single mode in the spectrum of a meromorphic two-point function (in the complex frequency plane at fixed wavevector) in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation described by the hydrodynamic gradient expansion, known at least to some (preferably high) order. We first apply the algorithm to a simple algebraic example and then to the transverse momentum excitations in the holographic theory that describes a stack of M2 branes and includes momentum diffusion as its gapless excitation.
