论文标题
$ ϕ_4^4 $理论在半空间上的扰动重归化
Perturbative renormalization of $ϕ_4^4$ theory on the half space $\mathbb{R}^+ \times\mathbb{R}^3$ with flow equations
论文作者
论文摘要
在本文中，我们使用重新归一化的组流程方程式在半空间上进行了严格的$ ϕ_4^4 $理论的可误差的证明。我们发现需要进行五个反对意见来使理论有限，即$ ϕ^2 $，$ ϕ \ partial_z ϕ $，$ ϕ \ partial_z^2ϕ $，$ ϕδ_x $和$ ϕ^4 $ for $ for $（z，z，x）截肢的相关函数是位置空间中的分布。我们考虑了一类合适的测试功能，并证明了与这些测试功能折叠的相关函数的归纳界限。边界在截止中是均匀的，因此直接导致了重差。
In this paper, we give a rigorous proof of the renormalizability of the massive $ϕ_4^4$ theory on a half-space, using the renormalization group flow equations. We find that five counter-terms are needed to make the theory finite, namely $ϕ^2$, $ϕ\partial_zϕ$, $ϕ\partial_z^2ϕ$, $ϕΔ_xϕ$ and $ϕ^4$ for $(z,x)\in\mathbb{R}^+\times\mathbb{R}^3$. The amputated correlation functions are distributions in position space. We consider a suitable class of test functions and prove inductive bounds for the correlation functions folded with these test functions. The bounds are uniform in the cutoff and thus directly lead to renormalizability.
