# Regularization is mandatory. What about renormalization?

We need to regularize in order to declare with confidence that infinities drop out from measurable quantities, e.g. in the form of a cutoff scale. In general, the amplitudes in QFT depend on the regulator, e.g., the cutoff scale $$\Lambda$$: $$\Gamma = \Gamma(\mu, \Lambda)$$ where $$\mu$$ is the scale at which we evaluate the amplitude.

However, the difference between a given amplitude at two different energy scales is actually independent of $$\Lambda$$: $$\Gamma(\mu, \Lambda) - \Gamma(\mu', \Lambda) \propto \ln(\mu/\mu')\, .$$ In this sense, the regulator drops out from measurable quantities and with it the dangerous UV infinites.

Therefore, I was wondering if renormalization is really mandatory or just a convenient method to make calculations simple?

• Everything here seems backwards and confused. Regularization is not mandatory (e.g., some theories are naturally finite; moreover, if you consider fields to be distributions rather than functions, no infinities appear at any point, cf. Glaser-Epstein). Similarly, renormalisation has nothing to do with divergences, and it is not a "method"; rather, it is just the statement that non-linearities (either classical or QM; either finite or divergent) modify the parameters that appear in the linear theory, cf. physics.stackexchange.com/a/300734/84967 – AccidentalFourierTransform Jul 8 '19 at 13:58