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Renormalization

A procedure to handle infinities that arise in QED calculations, absorbing them into redefinitions of physical parameters like mass and charge.
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The statement of the theorem

The bare Lagrangian Lbare\mathcal{L}_{bare} is related to the renormalized Lagrangian Lren\mathcal{L}_{ren} by introducing counterterms δZi\delta Z_i: Lbare=Lren+Lcounter=Lren+12δZ3Fμν□−1Fμν+δZmψˉψ+…\mathcal{L}_{bare} = \mathcal{L}_{ren} + \mathcal{L}_{counter} = \mathcal{L}_{ren} + \frac{1}{2} \delta Z_3 F_{\mu\nu} \Box^{-1} F^{\mu\nu} + \delta Z_m \bar{\psi} \psi + \dots The physical parameters (mphys,ephysm_{phys}, e_{phys}) are obtained by absorbing the infinities (∝Λ\propto \Lambda) into these counterterms, ensuring that the physical observables remain finite.