Li Wenliang
School of Physics, Sun Yat-Sen University, Guangzhou 510275, China.
Phys Rev Lett. 2023 Jul 21;131(3):031603. doi: 10.1103/PhysRevLett.131.031603.
In quantum field theory, the Dyson-Schwinger equations are an infinite set of coupled equations relating n-point Green's functions in a self-consistent manner. They have found important applications in nonperturbative studies, ranging from quantum chromodynamics and hadron physics to strongly correlated electron systems. However, they are notoriously formidable to solve. One of the main obstacles is that a finite truncation of the infinite system is underdetermined. Recently, Bender et al. [Phys. Rev. Lett. 130, 101602 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.101602] proposed to make use of the large-n asymptotic behaviors and successfully obtained accurate results in D=0 spacetime. At higher D, it seems more difficult to deduce the large-n behaviors. In this Letter, we propose another avenue in light of the null bootstrap. The underdetermined system is solved by imposing the null state condition. This approach can be extended to D>0 more readily. As concrete examples, we show that the cases of D=0 and D=1 indeed converge to the exact results for several Hermitian and non-Hermitian theories of the gϕ^{n} type, including the complex solutions.
在量子场论中，戴森 - 施温格方程是一组无穷的耦合方程，它们以自洽的方式关联n点格林函数。这些方程在非微扰研究中有着重要应用，范围涵盖从量子色动力学、强子物理到强关联电子系统。然而，求解这些方程是出了名的困难。主要障碍之一是无穷系统的有限截断是欠定的。最近，本德等人[《物理评论快报》130, 101602 (2023)PRLTAO0031 - 900710.1103/PhysRevLett.130.101602]提议利用大n渐近行为，并在D = 0时空成功获得了精确结果。在更高的D值下，推导大n行为似乎更加困难。在本快报中，我们根据零引导提出了另一条途径。通过施加零态条件来求解欠定系统。这种方法可以更轻松地扩展到D > 0的情况。作为具体例子，我们表明对于几种gϕⁿ型的厄米和非厄米理论，包括复解，D = 0和D = 1的情况确实收敛到精确结果。
