流方程格点正则化$ϕ_4^4$的微扰重整化
Perturbative renormalization of the lattice regularized $ϕ_4^4$ with flow equations
摘要：
重整化群的流方程允许分析可重整化量子场论的微扰$n$ -点函数。严格的界限意味着重正化允许控制大的动量行为，红外奇异性和大的顺序行为的循环数和参数$n$的数量。本文用格点正则化方法分析了欧几里德$4$维有质量$ϕ_4$理论.我们提出了一个严格的证明，这量子场论是重整化，所有订单的循环扩展的基础上的流动方程。众所周知，格子打破了时空的欧几里得对称性。我们的主要结果是证明恢复的欧几里德对称性使用流方程。
英文摘要：
The flow equations of the renormalization group allow to analyse the perturbative $n$-point functions of renormalizable quantum filed theories. Rigorous bounds implying renormalizability permit to control large momentum behaviour, infrared singularities and large order behaviour in the number of loops and the number of arguments $n$. In this paper, we analyse the Euclidean $4$-dimensional massive $ϕ_4$-theory using lattice regularization. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion based on the flow equations. The lattice is known to break the Euclidean symmetry of the space-time. Our main result is the proof of the restoration of the Euclidean symmetries using the flow equations.
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