近日，荷兰乌得勒支大学的Sofia Canevarolo及其研究团队取得一项新进展。经过不懈努力，他们实现了量子有效作用的梯度修正。相关研究成果已于2024年12月4日在国际知名学术期刊《高能物理杂志》上发表。
该研究团队为相互作用标量场理论推导出了梯度展开至二阶、且达到两圈阶的量子有效作用量。这种有效作用量的展开对于研究宇宙学背景下，空间或时间梯度起重要作用的问题（如一阶相变中的气泡成核）非常有用。假设背景场是时空依赖的，研究人员在维格纳空间中进行工作，并执行中点梯度展开，这与传播子所满足的运动方程是一致的。
特别地，研究人员考虑到了这样一个事实：传播子受到由对称性要求得出的额外运动方程的非平凡约束。在单圈阶，研究人员首先展示了单标量场情况下的计算，然后将结果推广到多场情况。虽然在单场情况下他们发现结果为零，但在考虑多场时，单圈二阶梯度修正可能是显著的。
作为示例，研究人员将结果应用于一个包含规范动能项和树级质量混合的，两个标量场的简单玩具模型。最后，他们计算了单标量场情况下的两圈单粒子不可约（1PI）有效作用量，并得到了一个不可重整化的结果。通过添加双粒子不可约（2PI）反项，理论变得可重整化，这表明当在微扰理论中使用重求和的1PI两点函数时，2PI形式主义是重整化的正确框架。
附：英文原文
Title: Gradient corrections to the quantum effective action
Author: Canevarolo, Sofia, Prokopec, Tomislav
Issue&Volume: 2024-12-04
Abstract: We derive the quantum effective action up to second order in gradients and up to two-loop order for an interacting scalar field theory. This expansion of the effective action is useful to study problems in cosmological settings where spatial or time gradients are important, such as bubble nucleation in first-order phase transitions. Assuming spacetime dependent background fields, we work in Wigner space and perform a midpoint gradient expansion, which is consistent with the equations of motion satisfied by the propagator. In particular, we consider the fact that the propagator is non-trivially constrained by an additional equation of motion, obtained from symmetry requirements. At one-loop order, we show the calculations for the case of a single scalar field and then generalise the result to the multi-field case. While we find a vanishing result in the single field case, the one-loop second-order gradient corrections can be significant when considering multiple fields. As an example, we apply our result to a simple toy model of two scalar fields with canonical kinetic terms and mass mixing at tree-level. Finally, we calculate the two-loop one-particle irreducible (1PI) effective action in the single scalar field case, and obtain a nonrenormalisable result. The theory is rendered renormalisable by adding two-particle irreducible (2PI) counterterms, making the 2PI formalism the right framework for renormalization when resummed 1PI two-point functions are used in perturbation theory.
DOI: 10.1007/JHEP12(2024)037
Source: https://link.springer.com/article/10.1007/JHEP12(2024)037