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Renormalization

A procedure to handle infinities that arise in calculations within QFT, allowing for finite and physically meaningful results.
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The statement of the theorem

Consider a bare Lagrangian L0\mathcal{L}_0 and the renormalized Lagrangian LR\mathcal{L}_R. The renormalization procedure requires defining counterterms LCT\mathcal{L}_{CT} such that the physical observables remain finite. For a field ϕ\phi, the bare field ϕ0\phi_0 is related to the renormalized field ϕ\phi by ϕ0=Zϕ1/2ϕ\phi_0 = Z_{\phi}^{1/2} \phi, and the bare coupling g0g_0 is related to the renormalized coupling gg by g0=Zggg_0 = Z_g g. The requirement is that the renormalized amplitude MR\mathcal{M}_R is finite: MR=finite\mathcal{M}_R = \text{finite}.
Source: Wikipedia