论文标题
在字符串启发的非本地场理论中的轮廓处方
On the contour prescriptions in string-inspired nonlocal field theories
论文作者
论文摘要
在量子场理论中，需要在复杂能平面中定义和变形的整合轮廓的一致处方，以评估环路积分和计算散射幅度。在某些非局部场理论（包括字符串场理论）中，相互作用顶点包含可以沿着某些复杂方向发散的动量的先验函数，因此无法使用标准技术（例如wick旋转）来执行循环积分。本文的目的是研究在存在非局部顶点的情况下几种轮廓处方的可行性。我们考虑三种``不同''处方，并在本地和非本地理论中建立了它们的（在）等效性。特别是，我们证明所有这些处方在标准的本地理论中都是等效的，而对于非局部理论的情况并非如此，在这种非本地理论中，必须首先在欧几里得空间中定义幅度，然后分析地继续进行Minkowski。我们在一环级别工作，并专注于气泡图。除了证明大量非本地理论的一般结果外，我们还显示了字符串启发的非局部标量模型的明确计算。
In quantum field theory, a consistent prescription to define and deform integration contours in the complex energy plane is needed to evaluate loop integrals and compute scattering amplitudes. In some nonlocal field theories, including string field theory, interaction vertices contain transcendental functions of momenta that can diverge along certain complex directions, thus making it impossible to use standard techniques, such as Wick rotation, to perform loop integrals. The aim of this paper is to investigate the viability of several contour prescriptions in the presence of nonlocal vertices. We consider three ``different'' prescriptions, and establish their (in)equivalence in local and nonlocal theories. In particular, we prove that all these prescriptions turn out to be equivalent in standard local theories, while this is not the case for nonlocal theories where amplitudes must be defined first in Euclidean space, and then analytically continued to Minkowski. We work at one-loop level and focus on the bubble diagram. In addition to proving general results for a large class of nonlocal theories, we show explicit calculations in a string inspired nonlocal scalar model.
