# MS Renormalization: Questions & Answers

• RedX
In summary, the residue R comes into play because it is the square root of the propagator residue at the physical mass.
RedX
I have a question about the MS renormalization scheme. When you choose this scheme, all sorts of strange things start happening. The mass in your Lagrangian can no longer be the physical mass. The 4-momentum of a physical particle squares to the physical mass, not the free-field mass. But what I don't get is why the creation and annihilation operators get divided by the square root of the residue of the propagator at the physical mass. How does this happen?

I'm not sure I know what you're asking. Very generally, if the residue of the pole in the propagator is Z, then you need a factor of Z^(-1/2) multiplying each field in the LSZ formula for the scattering amplitude. See e.g. P&S eq.(7.42) (where they have Z^(1/2) times the scattering ampliude instead of Z^(-1/2) times the field).

I was looking at page 173 of MS's book where he talks about the MS scheme (Mark Srednecki). He writes that " $$Z^{\frac{-1}{2}}\phi(x)$$ now has unit amplitude to create a one-particle state ".

The creation and annihilation operators are usually the Fourier coefficients of the free-field solutions, solved in terms of the field. But from the derivation of the LSZ forumula, you should really insert the renormalized field into the expression for the creation and annihilation operators, and not the bare fields. But although that might explain factors of $$Z_{\phi}$$, how does the residue R come into play?

I'll see if I can find a preview of P&S online from google books - my library doesn't have it.

Okay, thanks, I figured it out from those pages of PS you suggested. I like MS's interpretation better, but I only understood what MS was saying after I read the pages of PS you gave. I was able to reconcile MS's and PS's interpretation.

## 1. What is MS Renormalization?

MS Renormalization is a mathematical technique used in theoretical physics to eliminate infinities that arise in quantum field theories. It involves adjusting the parameters of a theory to match experimental results at a specific energy scale, known as the renormalization scale.

## 2. Why is MS Renormalization important?

MS Renormalization is important because it allows us to make accurate predictions in quantum field theories, which are essential for understanding the fundamental forces of nature. Without this technique, many theories would be plagued by infinities and would not be able to accurately describe real-world phenomena.

## 3. How does MS Renormalization work?

MS Renormalization works by introducing a new constant, known as the renormalization constant, which absorbs the divergences that arise in the theory. This constant is then adjusted to match the observed values at the chosen renormalization scale, effectively removing the infinities and allowing for accurate predictions.

## 4. What is the difference between MS Renormalization and other renormalization schemes?

MS Renormalization is a specific type of renormalization scheme, known as the minimal subtraction scheme. It differs from other schemes in that it preserves the original form of the theory's equations, making it easier to work with mathematically.

## 5. Are there any limitations to MS Renormalization?

While MS Renormalization is a powerful tool, it does have its limitations. It is most effective for theories that are perturbative, meaning they can be approximated by a series of calculations. It also only works for theories that are renormalizable, meaning they have a finite number of parameters that need to be adjusted.

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