$ϕ^4$理论中NLO散射的有限系统尺寸修正
Finite System Size Correction to NLO Scattering in $ϕ^4$ Theory
摘要：
我们在质量$ϕ^4$理论中计算了从$\mathbb R^{1,m}\times T^n$到NLO的$2\rightarrow2$散射。我们使用“分母正则化”代替通常的维数正则化来进行计算，这允许$T^n$的非对称配置。给出了广义Epstein zeta函数解析延拓的一个透明的推导过程和方程。我们证明了光学定理是满足的，推广了Hardy关于平方计数函数的一个猜想。我们评论的影响。
英文摘要：
We compute $2\rightarrow2$ scattering in massive $ϕ^4$ theory on $\mathbb R^{1,m}\times T^n$ to NLO. We perform the calculations using "denominator regularization" instead of the usual dimensional regularization, which allows for asymmetric configurations of the $T^n$. We give a transparent derivation of and equation for the analytic continuation of the generalized Epstein zeta function. We show that the Optical Theorem is satisfied and generalize a conjecture by Hardy on square counting functions. We comment on the implications.
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