# 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 what's going on in the provided solution). It's possible that...

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 ##...

31. ### Transformation from de Sitter to flat spacetime coordinates

You were right, there is a minus sing missing and with it everything works out... Thanks for the help!
32. ### Transformation from de Sitter to flat spacetime coordinates

Let me begin by stating that I'm aware of the fact that this is a metric of de Sitter spacetime, aka I know the solution, my problem is getting there. My idea/approach so far: in the coordinates ##(u,v)## the metric is given by $$g_{\mu\nu}= \begin{pmatrix}1 & 0\\ 0 & -u^2\end{pmatrix}.$$ The...
33. ### Wick contraction in scalar QED

While writing out the Dyson series due to the time ordering above I encountered the two expressions $$T(\mathcal{L}_{int}(x))\quad \text{and}\quad T(\mathcal{L}_{int}(x)\mathcal{L}_{int}(y))$$ I was able to write out the first term in terms of contractions using Wick's theorem and then finally...

36. ### Nother current of given symmetry

Thank you very much for the detailed answer! I tried using your approach on a problem which I already solved, to see if I really understood it.. Unfortunately I'm still struggling. Lets say I have a vector field ##A_\mu## and I consider only a translation, aka something of the form...
37. ### Nother current of given symmetry

First of all, thank you for the reply. I'd like to split the following question into two parts: Assuming that ##\mathcal{L}## is scale-invariant (aka ##m## and ##\mu## are zero and the values of ##\lambda## and ##\Delta## chosen accordingly). In this case we have ##\delta\mathcal{L}=0##, which...
38. ### Show that the given Green Function is the propagator of a certain Lagrangian

After some trying out I was able to obtain a partial result I think. First derive the EoM for the given Lagrangian, which results in $$\partial^2 A^\rho -\partial^\rho\partial^\lambda A_\lambda + \xi^{-1}\partial^\rho\partial^\lambda A_\lambda=0.$$ Now we can apply the following trick to get...

42. ### Covariant derivative of a (co)vector field

I don't know. Usually I'd say the "derivative" of a constant is zero, but I'm really not sure if this is true when talking about the covariant derivative... The only things I know about this derivative are written above, and we defined ##\nabla_{\partial_i}\partial_j :=...
43. ### Covariant derivative of a (co)vector field

I'm sorry, I can't follow you... I mean we then would have ##\nabla _X (dx^a (\partial_b))= \nabla_X \delta^a_b = X^i\nabla_{\partial_i}\delta^a_b##. But what now? Also, why exactly are we considering this? I mean, there is a difference between ##\nabla _X (dx^a (\partial_b)) ## and ##(\nabla _X...
44. ### Covariant derivative of a (co)vector field

I think it's ##\nabla_X (dx^a(\partial_a)) = \nabla_X \delta^a_a = \nabla_X##, or isn't it?

48. ### Global Positioning System / Clocks in Space

Thank you for the answer and the hints. Up until now we have only been doing special relativity, slowly starting to move towards general relativity by introducing acceleration in inertial frames (e.g. the exercise you helped me solve last weekend about orbits of particles with constant...
49. ### Global Positioning System / Clocks in Space

I'm a bit lost at how to exactly start this exercise... As far as I understand we need to first determine ##d\tau_E## and ##d\tau_S##. First question: Since we can neglect the Earth's movement, can I also neglect the movement of the satellite with respect to the far away observer? If so, I...
50. ### Acceleration in special relativity

Thanks for the hint, but this time I didn't work because I again didn't pay enough attention to the details... The differential equation, with the same boundary condition, is actually \frac{dv}{dt} = {\left(1-\frac{v^2}{c^2}\right)^{3/2}}a'\quad\Longrightarrow \quad...