Maybe, but at the same time it seems we're perfectly happy doing pertubation theory with terms that are literally infinite, but that's okay because the infinities cancel. Similarly, can't I just choose ##\log\left( \mu /E\right)## as large as I want knowing that all ##\mu## dependence cancels...
I have a question about the ##\mu## in dimensional regularization and how it is related to renormalization conditions. I follow the same notation and conventions as in Schwartz. Take QED as an example:
$$\mathcal{L} =-\frac{1}{4}\left( F_{0}^{\mu \nu }\right)^{2} +\overline{\psi }_{0}\left(...