# Search results

1. ### I How to determine matching coefficient in Effective Field Theory?

Assume that I have the Lagrangian $$\mathcal{L}_{UV} =\frac{1}{2}\left[\left(\partial_{\mu} \phi\right)^{2}-m_{L}^{2} \phi^{2}+\left(\partial_{\mu} H\right)^{2}-M^{2} H^{2}\right] -\frac{\lambda_{0}}{4 !} \phi^{4}-\frac{\lambda_{2}}{4} \phi^{2} H^{2},$$ where ##\phi## is a light scalar field...

4. ### Mass correction in ##\phi^4##-theory

@vanhees71 Thanks a lot for the explanations and I will be sure to check out your lecture notes! Just as a quick check, the issue is that I basically conflated the following, right? i.e. I assumed that ##\phi^4## has this one extra loop diagram that appears due to a ##\phi^3## interaction...
5. ### Mass correction in ##\phi^4##-theory

Alright, this makes sense. Then we have $$m_{\text{ren}}^2=m^2[1+I(m_{\text{ren}}^2)] \approx m^2[1+I(m^2)].$$ When exactly did that happen? Where in post #1 did I make a mistake so that I ended up in ##\phi^3## theory?

9. ### Conservation law for FRW metric

My attempt: Realize we can work in whatever coordinate system we want, therefore we might as well work in the rest frame of the fluid. In this case ##u^a=(c,\vec{0})##. The conservation law reads ##\nabla^a T_{ab}=0##. Let us pick the Levi-Civita connection so that we don't have to worry about...
10. ### Covariant derivative and the Stress-enegery tensor

Perfect, thanks a lot for checking and looking up the references!

16. ### I How to determine Spinor in Feynman diagram

Isn't this just a matter of definition? My lecturer demands that we use ##v_\alpha## for electrons (created and annihilated by ##a^\dagger## and ##a##) and ##u_\alpha## for positrons (created and annihilated by ##b^\dagger## and ##b##), which unfortunately makes looking up stuff sometimes really...
17. ### I How to determine Spinor in Feynman diagram

Consider Moller scattering, that is $$e^-(\vec p_1, \alpha)+e^-(\vec p_2, \beta) \quad\longrightarrow\quad e^-(\vec q_1, \gamma)+e^-(\vec q_2, \delta),$$ where the ##\vec{p}_i,\vec q_i## label the momenta of the in and outgoing electrons and the greek letter the spin state. The two relevant...
18. ### I Normal order and overlap of states

Thank you very much @HomogenousCow I think this clears up my confusion about the topic.
19. ### I Normal order and overlap of states

The second sentence is exactly what confuses me! When you say "we need [...] to contract with the creation annihilation operators outside of the time ordering sign", what exactly do you mean with the "contract"? Up to now I thought that contractions can only arise in the context of Wick's...
20. ### I Normal order and overlap of states

@HomogenousCow Thank you for the answer. Maybe I'm misunderstanding you, but the exercise was supposed to be solved in the way I presented above, so I cannot just change that (I technically could, but I would like to understand whats going on in the provided solution). It's possible that I...

28. ### I Consfused about the workflow for calculating scattering amplitudes with Feynman diagrams

In the following I will try to deduce the scattering amplitude for a specific interaction. My question is at the bottom, the entire rest is my reasoning to explain how I came to the results I present. My working Let's assume I would like to calculate the second order scattering amplitude in ##...