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Renormalization

Renormalization is a mathematical procedure used to handle infinities that arise in calculations within the theory, ensuring finite results.
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The statement of the theorem

Consider a divergent quantity O\mathcal{O} calculated via loop diagrams, yielding O=Ofinite+Odivergent\mathcal{O} = \mathcal{O}_{finite} + \mathcal{O}_{divergent}. Renormalization requires defining the bare parameters (λ0,m0,Zi\lambda_0, m_0, Z_i) such that the physical, measurable quantities (λ,m,Zi\lambda, m, Z_i) are finite. This is achieved by introducing counterterms LCT\mathcal{L}_{CT} into the Lagrangian: \nLbare=Lrenormalized+LCT\mathcal{L}_{bare} = \mathcal{L}_{renormalized} + \mathcal{L}_{CT} \nWhere LCT\mathcal{L}_{CT} cancels the infinities arising from the loop integrals, e.g., LCT=∑iδZiLi\mathcal{L}_{CT} = \sum_i \delta Z_i \mathcal{L}_i, ensuring that the renormalized Green's functions are finite.
Source: Wikipedia