非高手 但係我嘅理解係
1. 從effective field theory 角度嚟睇, 個theory 會 diverge (in the UV) 主要係因為我哋太自大, 以為個theory works in all energy scale。當然真實上唔係咁 所以我地需要 “parametrize our ignorance”, 例如用一個hard cut off 表示喺呢個 cut off之上,我哋個theory就唔work。當然你真正計數時要顧及好多問題, 例如你個regularisation scheme 係唔係consistent with the theory’s symmetry, 不過個philosophy冇變到 - 你係modify緊個theory嘅 UV structure。理論上high energy behaviours 係唔會影響到 low energy physics (所謂嘅 “decoupling”),所以我哋expect 最尾嘅答案應該係 regulator-independent。(不過唔一定, 請參考 UV-IR mixing)
2. 而Renormalization 則係我哋計physical observable嘅時候唔記得咗lagrangian 入面嘅parameters (例如mass/ coupling constant) 其實係冇被define過。所以當我哋express observable should in terms of “bare” parameters, 個expression係冇意思。我哋首先要 define 啲 parameters (所謂嘅 “renormalization scheme”) 去令到佢哋physically meaningful, 然後express observables in terms of physical parameters。呢個過程就係renormalization。個idea係 lagrangian parameters係你個theory嘅input,當你喺某個energy scale 度咗佢哋之後,你就可以make predictions。
當然有人會覺得咁樣做其實係多舊魚,理論上應該有方法直接計finite results而唔使做咁多intermediate steps,詳情可以查下 “causal perturbation theory”。我唔熟呢方面所以我唔想亂噏
Sor for 1999
