Recent content by JILIN

Oh, finally I understand! Thank you very much, Avodyne!

I appreciate your kind discussion (at the same time I'm sorry that I'm slow to understand). I agree that ##\rho(s)=0## and ##\mathrm{Im}\Pi(-s)=0## for ##4m^2>s \ne m^2##. But at ##s=m^2##, I think that an additional condition ##\mathrm{Re}\Pi(-m^2)=0## is needed; this condition and...

Integral over ##s## in eq. (15.8) does not necessarily need to start at ##4m^2##. It starts at ##4m^2## just because we know ##\rho(s)=0## for ##s<4m^2## (this is clearly seen around eq. (13.11) in chapter 13). Thus, eq. (15.8) and also eq. (15.13) is valid for any ##s## (or any ##-k^2##)...

Thanks, Avodyne. But my question is the following one. I think that eqs. (15.12) and (15.8) give ##\pi \rho (s) = \frac{\mathrm{Im}\Pi(-s)}{(k^2+m^2-\mathrm{Re}\Pi(-s))^2 + (\mathrm{Im}\Pi(-s))^2} - \pi \delta(-s+m^2),## instead of eq. (15.13) in his text.

Hi. I would like to ask a question about Chapter 15 in Srednicki's QFT book. In chapter 15, after eq. (15.12), he compares eq. (15.12) ## \mathrm{Im}\bm{\Delta}(k^2)=\frac{\mathrm{Im}\Pi (k^2)}{(k^2+m^2-\mathrm{Re}\Pi (k^2))^2 + (\mathrm{Im}\Pi (k^2))^2}## with eq. (15.8)...

Thank you for your instructive comment!

Thank you, naima & Avodyne. I understand.

Thank you, naima. For "free" field, you are right. But now in chap. 9 we consider "interacting" field, and ##\phi (0)## is interacting one. Thus, I do not think we can use eqs. in chap. 3 to prove ##<p| \phi (0) |0>## is Lorentz-invariant. How about following one? For ##t=\pm \infty##...

Thank you very much! I understand 2 & 3, but sorry I do not fully understand 1. I think that the Lorentz-invariance of <p|\phi (0)|0> is important. <p|\phi (0)|0> should be just some number that is independent of p^\mu, and it is the Lorentz-invariance that makes <p|\phi (0)|0> be, i.e...

I have questions about chapters 5 & 9 in Srednicki's book. 1. Below eq. (5.18), he says "$<p|\phi (0)|0>$ is a Lorentz-invariant number.", but I do not know why. 2. Below eq. (5.26), he says "After shifting and rescailing (and renaming some parameters)". Are $m$ and $g$ in eq. (5.26)...