Anomalies in quantum field theories

Abstract

Introduction/purpose: Noether’s theorem connects symmetry of the Lagrangian to conserved quantities. Quantum effects cancel the conserved quantities. Methods: Triangle diagram, Path integral, Pauli-Villars regularisation. Results: Quantum effects that spoil conserved quantities of local gauge symmetries endager renormalisability. Conclusion: A careful treatment of anomalies is needed in order to obtain correct results. The π0 → γγ decay is perhaps the most notable “impossible” effect allowed by anomalies.

Keywords

• symmetry
• quantum anomalies