Physics - Quantum Field Theory - Renormalization and running couplings - Renormalization: From Problem to Principle

5-step lesson. Step 1: 'The problem: Loop integrals in QFT diverge. Example: electron self-energy Σ(p) = ∫d⁴k [propagator × vertex × propagator] → ∫dk/k → ln(Λ) → ∞ as cutoff Λ→∞. Similarly: vacuum polarization, vertex correction. These shift the mass, charge, and field normalization by infinite amo