# Error in Srednicki renormalization?

• Higgsy
In summary, Srednicki discusses renormalization schemes in Chapter 27 of his book. In this chapter, he derives an equation for the squared mass of a particle, which involves a logarithmic term and a coefficient. However, after taking a log and dividing by 2, he notices that the logarithmic term does not have a coefficient. This is because he is using the relation that ln(1 + x) = x + O(x^2), where x contains an alpha term. Therefore, the O(x^2) term is absorbed into the O(alpha^2) term.
Higgsy
On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$

But after taking a log and dividing by 2 he arrives at
$$ln[m_{ph}] = ln[m] \left [ \left ( \frac{5}{12}\alpha(ln \frac{\mu}{m}) +\frac{1}{2} c' \right ) + O(\alpha^2)\right]$$

Why is there no ln on the $$\frac{5}{12} \alpha$$ term?

He is using the relation
$$\ln(1 + x) = x + O(x^2)$$
Here ##x## has an ##\alpha## in it, so the ##O(x^2)## term is absorbed into the ##O(\alpha^2)##.

Higgsy and bhobba
Thanks!

## 1. What is the Srednicki renormalization procedure?

The Srednicki renormalization procedure is a method used in quantum field theory to remove the effects of ultraviolet divergences in calculations. It involves introducing a cutoff parameter to limit the high energy contributions and then taking the limit as the cutoff goes to infinity.

## 2. What is the source of error in the Srednicki renormalization procedure?

The main source of error in the Srednicki renormalization procedure is the choice of the cutoff parameter. Different cutoff values can lead to different results, and the limit of the cutoff going to infinity is not always well-defined.

## 3. How is the error in Srednicki renormalization minimized?

The error in Srednicki renormalization can be minimized by choosing a physically motivated cutoff parameter and carefully considering the limits of the cutoff going to infinity. Additionally, performing calculations using different cutoff values and comparing the results can help to identify any potential errors.

## 4. Are there any alternative methods to Srednicki renormalization?

Yes, there are alternative methods to Srednicki renormalization, such as dimensional regularization and lattice regularization. These methods also aim to remove ultraviolet divergences in quantum field theory calculations, but they use different techniques and may produce different results.

## 5. Is the Srednicki renormalization procedure reliable?

The reliability of the Srednicki renormalization procedure depends on the specific situation and the choice of cutoff parameter. In some cases, it may lead to accurate and physically meaningful results, but in others, it may introduce errors and inconsistencies. It is important to carefully consider the limitations and assumptions of the procedure when using it in calculations.

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