Is renormalization prescription and renormalization scheme the same thing?

Question

Renormalization group functions are different but related under different renormalization schemes, for example between CW scheme and MS scheme.

There is also a special chapter 'Renormalization-prescription dependence' in John. C. Collins's book about renormalization.

Is renormalization prescription and renormalization scheme the same thing?

Comments

Good question, coming more from a Wilsonion EFT and RG flow point of view, these term that go along with the subtraction business confuse me too, in fact it reminds me that I wanted to ask a question about the differences between the two methods i... I always thought that the prescription is the higher energy initial condition one starts with to calculate lower energy quantities by using a certain course-graining method called a renormalization scheme.

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@Dilaton Why didn't you make the last part an answer? 

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@dilaton could you make this into an answer?

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Yes, but later when I have my laptop available and I also want to take the time to properly extend the relevant part of the comment a bit ...

Answer 1

This is a semantic question. 

A renormalization scheme is nothing more than a renormalization procedure. For example, Minimal Subtraction and momentum-space subtraction (subtraction for given values of Mandelstam variables) are examples of different renormalization schemes. 

Renormalization prescriptions are often used to distinguish between two different subtractions points in momentum space (two sets of Mandelstam variables) within momentum-space subtraction. For example, one can sometimes make use of a prescription such that the renormalized mass is equal to the physical mass (on-shell prescription) whereas for other problems subtracting a diagram at $p=0$ can be more convenient. One can think of different prescriptions as different initial conditions.

Comments

If the renormalized mass is equal to the physical mass (on-shell prescription), then it is clear that the real (physical) mass belongs to an interacting electron, not to a free one - because you take the interaction into account. Free is the resulting compound system - a "dressed" electron, right? Isn't it like a "dressed" nucleus in atom?