In Peskin at page 248 he finds that if he calculates the vacuum polarization that(adsbygoogle = window.adsbygoogle || []).push({});

$$\Pi(q)^{\mu \nu} \propto g^{\mu \nu}\Lambda^2$$

a result which violates the Ward identity and would cause a non-zero photon mass $$M \propto \Lambda$$. But as Peskin states, the proof of the Ward identity is not valid when it requires a shift of integration variable and that is not a valid operation when the integral is divergent.

He then states that it is a way to rescue the Ward identity; namely trough dimensional regularization - a regularization method which respects the ward identity.

He then goes on and calculates the vacuum polarization and finds it respects the Ward identity.

I am however left a bit confused; it seems to be a choice which regulator to use and thus what mass the photon will get. Since the proof of the Ward identity does not hold for divergent integrals there seems to be no apriori reason to choose dimensional regularization other than to fit the theory to experiment.

So are we really left with a choice here?

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# Does the Ward identity rescue a zero photon mass?

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