Anomalies

• A QFT can possess both global and local continuous symmetries. In your opinion, is there any qualitative difference between the two?
• Explain what is an anomaly and how it shows up in a QFT. How can it happen that a symmetry of the classical system is violated by a quantum effect?
• Derive the naive Ward identity associated to the global axial U(1)_A in massless QED and satisfied by the generating functional of 1PI functions (assume invariance of the functional measure).
• Review the computation of the triangle diagram that invalidates the naive Ward identity.
• Convince yourself that the result cannot be expressed as a variation, under U(1)_A, of a local and U(1)_em invariant functional of the fields.
• What is the content of the Adler-Bardeen theorem?