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### Is the fact that the sum of all natural numbers $\sum_{n=1}^\infty n = -\frac{1}{12}$ essential to the understanding of the Casimir Force In QED?

Apparently this result is used in many areas physics including the extra dimensions of string theory, which is not the scope of the question. The result is apparently also used to understand the ...
1k views

### What is a logarithmic divergence?

I am reading about renormalisation in QED and I come across the term logarithmic divergence several times. Can somebody explain to me about it in simple terms?
157 views

### Radiative correction to the charge form factor $F_1$ in QED

In QED, one can calculate the correction to the form factor $F_2$. To the lowest order, $F_1=1$ and $F_2=0$. At one loop, it is found that $F_2(0)$ receives a non-zero finite correction which is ...
206 views

### What are the observable effects of finite pieces of the loop corrections in QED?

I'm lost amidst the calculation of regularization and renormalization process in QED. In addition to the divergent piece in the in the self-energy correction (similarly in vacuum polarization ...
184 views

### A derivative about chiral current in Peskin's book

In Peskin's book (an introduction to QFT), Page 655, the axial vector current is defined as follows, \begin{eqnarray*} j^{\mu5} & = & \text{symm }\lim_{\epsilon\rightarrow0}\bigg\{\bar{\psi}(x+...
223 views

### Divergent diagrams in QED

I was reading about how to choose divergent diagrams in QED by using the concept of Superficial degree of divergence. We have an empirical relation $$D= 4-E_b -\frac{3}{2}E_f$$ where $E_b$ is number ...
109 views

I review my QFT lecture notes and I am having hard times to figure out the significance of Ward identity in vacuum polarization. In class, we calculated one loop correction stated as $$i\Pi^{\mu\... 1answer 130 views ### How do logarithms show up in the one loop calculation of the vacuum polarization in QED? I am following Peskin with the computation of the vacuum polarization in QED and there is one thing I do not see. Equation (7.90) reads$$\frac{-8e^2}{(4\pi)^{d/2}}\int_0^1dx\,x(1-x)\frac{\Gamma(2-\...
Let's have diagrams in QED when we don't use Feynman gauge. Then the bare photon propagator will look like  \tag 1 D_{\mu \nu}(p) = -\frac{g_{\mu \nu} - \frac{p_{\mu}p_{\nu}}{p^{2}}}{p^{2} + i\...