Richard Feynmann, Relativistic Cut Off For Quantum Electrodynamics, 1948

Beschreibung

Key Contributions: Finite Self-Energy Solution: Feynman introduces a relativistically invariant cut-off method to eliminate divergences in quantum electrodynamics (QED). By replacing the standard spectral density  δ ( ω 2 − k 2 ) δ(ω  2  −k  2  ) with a smoothed function  g ( ω 2 − k 2 ) g(ω  2  −k  2  ), he derives a finite self-energy for a free electron. The cut-off function subtracts high-frequency contributions (à la Bopp), yielding results consistent with mass renormalization prescriptions by Bethe, Weisskopf, and Schwinger. Agreement with Empirical Predictions: Line shifts for bound electrons match Bethe’s non-relativistic calculation. Radiationless scattering corrections align with Schwinger’s formalism, including the anomalous magnetic moment term  e 2 2 π ℏ c 2πℏc e  2   ​  . Unsolved Challenges: Vacuum polarization (Uehling terms) remains divergent under this cut-off. Proposes an alternative approach (inspired by Wataghin) to suppress light-cone singularities by modifying electron state densities. Methodological Insights: The cut-off preserves Lorentz invariance and avoids introducing arbitrary fundamental lengths. Highlights the provisional nature of the model, viewing it as a scaffold for future theories (later realized via Feynman diagrams and renormalization).