论文标题

量子有效作用的梯度校正

Gradient corrections to the quantum effective action

论文作者

Canevarolo, Sofia, Prokopec, Tomislav

论文摘要

我们将量子有效作用得出最高梯度中的二阶,最多可提供两回合的订单,以进行相互作用的标量场理论。有效作用的这种扩展对于研究空间或时间梯度很重要的宇宙学环境中的问题有用,例如在一阶相变中的气泡成核。假设时空依赖背景字段,我们在Wigner空间中工作并执行中点梯度扩展,这与传播器满足的运动方程一致。特别是,我们考虑了一个事实,即传播器在非对称要求中获得的其他运动方程式在非温和的限制上。在单循环的情况下,我们显示了单个标量场的情况的计算,然后将结果推广到多场案例。虽然我们在单场情况下发现消失的结果,但考虑多个字段时,一环二阶梯度校正可能很重要。例如,我们将结果应用于具有规范动力学术语和树级质量混合的两个标量字段的简单玩具模型。最后,我们在单个标量场情况下计算两环单粒子不可约(1PI)的有效作用,并获得了违法的结果。该理论是通过添加两个粒子不可约(2PI)反对的术语术语,这使得2PI形式主义在扰动理论中使用了1PI两点函数时,成为重新归一化的正确框架。

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.

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