量子场论中的谱密度约束
Spectral density constraints in quantum field theory
摘要：
确定谱密度的结构对于理解任何量子场论（QFT）的行为都是重要的。然而，这些量的精确计算通常需要对理论进行完整的非微扰描述，这对于物理现实理论如量子色动力学（QCD）来说是目前未知的。然而，可以推断出关于这些量的间接信息。在本文中，我们展示了一种方法，用于限制与QFT传播子，其中涉及匹配的频谱表示的短距离扩展与传播子的算子乘积展开（OPE）的谱密度的形式。作为这个过程的一个应用，我们分析了$ϕ^4$ -理论中的标量传播子和QCD中的夸克传播子，并给出了对谱密度和OPE凝聚的约束。特别地，证明了QCD中夸克凝聚的微扰和非微扰贡献是可以分解的，并且非微扰贡献与标量谱密度连续分量的结构有关。
英文摘要：
Determining the structure of spectral densities is important for understanding the behaviour of any quantum field theory (QFT). However, the exact calculation of these quantities often requires a full non-perturbative description of the theory, which for physically realistic theories such as quantum chromodynamics (QCD) is currently unknown. Nevertheless, it is possible to infer indirect information about these quantities. In this paper we demonstrate an approach for constraining the form of spectral densities associated with QFT propagators, which involves matching the short distance expansion of the spectral representation with the operator product expansion (OPE) of the propagators. As an application of this procedure we analyse the scalar propagator in $ϕ^4$-theory and the quark propagator in QCD, and show that constraints are obtained on the spectral densities and the OPE condensates. In particular, it is demonstrated that the perturbative and non-perturbative contributions to the quark condensate in QCD can be decomposed, and that the non-perturbative contributions are related to the structure of the continuum component of the scalar spectral density.
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