Recent content by Higgsy

In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?

But does $$P^{2}$$ commute with$$e^{ipx}$$ or how can I perform this commutation?

In the srednicki notes he goes from $$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to $$H = \int d^{3}p\frac{1}{2m}P^{2}\tilde{a}^{\dagger}(p)\tilde{a}(p) $$ Where $$\tilde{a}(p) = \int \frac{d^{3}x}{(2\pi)^{\frac{3}{2}}}e^{-ipx}a(x)$$ Is this as simple as...

For the Gordon identity $$2m \bar{u}_{s'}(\textbf{p}')\gamma^{\mu}u_{s}(\textbf{p}) = \bar{u}_{s'}(\textbf{p}')[(p'+p)^{\mu} -2iS^{\mu\nu} (p'-p)_{\nu}]u_{s}(\textbf{p}) $$ If I plug in $\mu$=5, what exactly does the corresponding $(p'+p)^{5}$ represent? 4 vectors can only have 4 components so...

On page 235 of srednicki (print) it says to plug a solution of the form $$ \textbf{$\Psi$} (x) = u(\textbf{p})e^{ipx} + v(\textbf{p})e^{-ipx}$$ into the dirac equation $$ (-i\gamma^{\mu} \partial_{\mu}+m)\textbf{$\Psi$}=0 $$ To get $$(p_{\mu}\gamma^{\mu} + m)u(\textbf{p})e^{ipx} +...

Thanks!

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...

What is the intuition behind divergences for the sunset diagram? I know that there is quadratic divergence by why no quartic divergence or higher?

Does anyone know any good references for discussion of ##\overline{MS}## theory in phi^4 theory?

Oh that makes sense. When would we be interested in the off-shell N-point function?

As I understand it, the 2-point fnuction is for 1 particle incoming, 1 particle outgoing. The 4-point function is for 2 particles incoming, 2 particles outgoing. Is this correct? So an N-point function describes N/2 incoming particles and N/2 outgoing particles? Thanks!

Srednicki. But these are not calculated in srednicki. To clarify, they are the vacuum feynman diagrams for $$\phi ^{4}$$ scalar theory

Given a diagram, how is one supposed to apply the feynman rules to calculate the feynman amplitude?

For quartic scalar field theory these are some of the lowest order diagrams (taken from the solutions to 9.2 srednicki). I'm wondering if someone can give me an intuition of how to actually calculate them. What I'm thinking is that vertices are $$\int \frac{d^{4}x}{(2\pi)^{4}}$$ and for the...

Oh right of course. Sorry it's getting late... thanks!