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Renormalization

Renormalization is a mathematical procedure used to handle infinities that arise in quantum field theories like the Standard Model.
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The statement of the theorem

Let L0\mathcal{L}_0 be the bare Lagrangian density containing bare parameters θ0\theta_0. Renormalization requires defining the renormalized Lagrangian LR\mathcal{L}_R such that L0=LR+LCT\mathcal{L}_0 = \mathcal{L}_R + \mathcal{L}_{CT}, where LCT\mathcal{L}_{CT} is the counterterm Lagrangian. The bare parameters are related to the physical (renormalized) parameters θR\theta_R and the counterterms δθ\delta\theta via θ0=θR+δθ\theta_0 = \theta_R + \delta\theta. The requirement that physical observables remain finite leads to the renormalization group equations (RGEs) for the running coupling constants αi\alpha_i: \nμdαidμ=βi(αi,… )\mu \frac{d\alpha_i}{d\mu} = \beta_i(\alpha_i, \dots) \nwhere μ\mu is the renormalization scale and βi\beta_i are the beta functions.
Source: Wikipedia