In learning QFT, I've found that the renormalization group is often introduced with the MS scheme. I noticed that if one uses the on-shell scheme instead and calculates the anomalous field dimension using(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\gamma_{\phi} = \mu \frac{\partial \ln Z_{\phi}}{\partial \mu} [/itex]

one finds that [itex]\gamma_{\phi} = 0[/itex]. Is this correct or am I making a mistake? What is the physical interpretation?

I've found this to be the case for both [itex]\phi^3[/itex] and [itex]\phi^4[/itex] theory. I haven't learned QED or anything about QFTs in particle physics so I'm not sure how it plays out there.

I wasn't sure if this is the place to post, or the homework or high-energy section; if this is not the right place, apologies and please feel free to move this thread.

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# A Anomalous field dimension in the on-shell scheme

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