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The most often discussed anomaly in the literature is the chiral anomaly, which as Fujikawa showed, may be understood as the non-invariance of the path integral measure under a symmetry transformation for which the classical action is invariant. Can all other quantum anomalies (conformal, trace, etc) be understood the same way, as due to the non-invariance of the path-integral measure?

As far as I could remember from reading the book "Quantum Theory of Fields" by Weinberg, in non-relativistic quantum mechanics, the mass parameter of a free particle is a central charge of the Galilean algebra. I am not sure if this anomaly has anything to do with path-integral. Also, in 2D CFT, there is the central charge of the virasoro algebra. But I have never seen that it is related with path-integral.

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