Quantum fluctuations at different momentum scales modify couplings, masses, and field normalizations. Renormalization reorganizes calculations so that physical predictions depend on measured observables rather than unphysical bare parameters. The renormalization group explains how theories flow under changes of scale.

A coupling $g(\mu)$ depends on the renormalization scale $\mu$ according to $\beta(g) = \mu\,\frac{dg}{d\mu}$. Fixed points satisfy $\beta(g_\ast)=0$ and control universal behavior near criticality or asymptotic regimes. Relevant, marginal, and irrelevant operators determine the structure of effective actions.

In an effective field theory, operators of higher mass dimension are suppressed by powers of a heavy scale $\Lambda$. Schematically, $\mathcal{L}_{\text{EFT}} = \mathcal{L}_{\text{ren}} + \sum_n \frac{c_n}{\Lambda^{n-4}}\mathcal{O}_n$. This parameterization captures unknown ultraviolet physics while retaining predictive low-energy control.

Renormalization is not merely a computational trick: it explains universality near phase transitions, scaling exponents, and why distinct microscopic systems can share the same infrared physics. In quantum field theory, it clarifies why low-energy predictions can be insensitive to unknown high-energy details.