7
votes
2answers
230 views

On the Axial Anomaly

I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
1
vote
0answers
153 views

Why does renormalization need an unbroken symmetry?

Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
20
votes
2answers
2k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views: Anomalies are due to the fact that quantum field ...
3
votes
1answer
504 views

Chiral anomalies à la Fujikawa: Why don't we just take another measure?

When deriving the chiral anomaly in the non perturbative approach for a theory of massless Dirac fermions, you start by showing that the path-integral measure is not invariant unter the chiral ...
12
votes
1answer
413 views

Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...