论文标题
功能性流动以进行复杂的有效动作
Functional flows for complex effective actions
论文作者
论文摘要
在目前的工作中，我们为计算复杂有效动作的计算建立了一个一般的功能重量级化组框架。对于明确的计算，我们考虑了Wilsonian有效作用的两个流以及一颗粒子不可约（1PI）的有效作用。后者是基于对复杂动作的Legendre变换的适当定义，我们通过与零维的确切结果进行比较，并与Wilsonian有效动作的结果进行了比较。在一般方法的当前实现中，威尔逊有效动作的流动具有更大的适用性，我们获得了$ ϕ^4 $理论中复杂领域的有效潜力的结果，从零到四个维度。这些结果还与1PI有效作用的结果相比，将其在其适用性范围内进行比较。复杂的有效动作还使我们能够确定Lee-Yang Zeros的一般参数值的位置。我们还讨论了当前结果的扩展到包括QCD在内的一般理论。
In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $ϕ^4$-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.
