论文标题
Wilsonian的交互方法$ ϕ^2（i ϕ）^\ varepsilon $
Wilsonian approach to the interaction $ϕ^2(iϕ)^\varepsilon$
论文作者
论文摘要
我们研究了非hermitian $ \ mathcal {p} \ Mathcal {t} $ - 对称标量场理论的重量量量量量，并使用wilsonian方法进行相互作用$ ϕ^2（ix）^\ varepsilon $，并且在$ \ varepsilon $中没有任何扩展。具体而言，我们在局部电势近似中求解了wetterich方程，无论是在紫外线方面和环路膨胀。我们计算规模依赖的有效潜力及其红外极限。仅对于$ \ varepsilon $的整数值，该理论在单循环级别上是可统一的，这一结果尚未在$ \ varepsilon $ -Expansion中建立。因此，要特别注意两个有趣的情况$ \ varepsilon = 1,2 $，并且计算了与交互相关的耦合$ ix^3 $和$ -DACE^4 $相关的耦合的单循环beta函数。发现$ -DECT^4 $理论在四维时空具有渐近自由。还得出了欧几里得分区功能和$ n $点功能的一些一般属性。
We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $ϕ^2(iϕ)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $iϕ^3$ and $-ϕ^4$ are computed. It is found that the $-ϕ^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.
