Student Friendly Introduction to QFT · Problem 12.3

Renormalization: Putting It All Together

Physics — QFT · mass-charge-renormalization-limits

Problem

Does it make sense to you that for our mass renormalization, we can have

\lim_{\Lambda\to\infty} \delta m = (\text{constant})\lim_{\Lambda\to\infty} e_0^2 \ln\frac{\Lambda}{m} = \infty

and

e_0^2 = 0

, whereas in our charge renormalization, we have

(\text{different constant})\lim_{\Lambda\to\infty} e_0^4 \ln\frac{k}{\Lambda} = e^2(k) = \text{finite}

and

e_0^2 = 0

? Why?