How do anomalies work in the causal formulation of QFT?

Question

In the Epstein-Glaser formulation of a QFT, the would-be divergences are taken care of by meticulously splitting the distributions that appear in the construction of the $S$-matrix (or correlation functions). As a result, there are no divergences anywhere and the theory is perfectly rigorous¹.

How do anomalies fit into this picture? These can be understood as the clash between a symmetry of the action and a regulator that refuses to respect it. In more pragmatical terms, the symmetry would be restored if the regulator is removed, so it is $\mathcal O(\epsilon^n)$, while the divergences are $\mathcal O(\epsilon^{-m})$; and, if $n=m$, a finite piece survives the physical limit $\epsilon\to 0$. But in the EG formulation, there are no divergences and no regulators, so how do anomalies arise? What is their precise role?

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^{1: and – naturally – it agrees, in a general sense, with what naïve perturbation theory predicts; formally speaking, in the EG formulation the would-be divergences are recast as polynomials in the external momenta, i.e., they are subtracted in momentum space, in the sense of BPHZ.}

Answer 1

Anomalies may (or may not) appear as obstructions in the proof of the Ward-Takahashi identities, which provide gauge invariance. See

D.R. Grigore, The structure of the anomalies of gauge theories in the causal approach, J. Physics A: Math. Gen. 35 (2002), 1665.

See also Chapter 15 (Interacting quantum fields) from the recent course ''Mathematical quantum field theory'' by Urs Schreiber.