（非）物理自由度的Källén-Lehmann光谱学
Källén-Lehmann spectroscopy for (un)physical degrees of freedom
摘要：
我们考虑的问题“测量”的Källén-Lehmann谱密度的粒子（无论是基本的或束缚态）的传播子通过4D点阵数据。由于后者是通过在（欧几里德动量平方）p^2>=0处的运算获得的，因此我们面临着将正实轴上的有限数据集转换为整个复p^2平面上的积分表示的一般不适定问题。我们采用线性正则化策略，通常称为具有Morozov差异原理的Tikhonov方法，对现实数据进行适当的调整，例如具有未知阈值。与（标准）最大熵方法相比，最大熵方法的一个重要优点是它还可以探测非物理的谱密度，例如，受限胶子的谱密度。我们在这里应用我们的建议，以“物理”模拟光谱数据作为试金石，然后在零温度下的格点SU（3）朗道规范胶子。
英文摘要：
We consider the problem of "measuring" the Källén-Lehmann spectral density of a particle (be it elementary or bound state) propagator by means of 4d lattice data. As the latter are obtained from operations at (Euclidean momentum squared) p^2>=0, we are facing the generically ill-posed problem of converting a limited data set over the positive real axis to an integral representation, extending over the whole complex p^2-plane. We employ a linear regularization strategy, commonly known as the Tikhonov method with Morozov discrepancy principle, with suitable adaptations to realistic data, e.g. with unknown threshold. An important virtue over the (standard) maximum entropy method is the possibility to also probe unphysical spectral densities, as, for example, of a confined gluon. We apply our proposal here to "physical" mock spectral data as a litmus test and then to the lattice SU(3) Landau gauge gluon at zero temperature.
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