Recent content by gobbles

Thank you TSny for the great explanation! I perfectly understand now.

Hmm.. the answer I consider to be correct (the dipole approach) is not my answer, I took it from a collection of problems and answers given here: http://www.princeton.edu/~xxiang/prelim/cahn/Cahn_part1.pdf This is question 2 from the Electrodynamics section. I see how the answer given there...

Thank you for your answers! The charged sphere polarizes the neutral one. The polarization density (=dipole density) is proportional to the electric field at the neutral sphere, caused by the charged sphere, so the second sphere behaves as a dipole ##\propto \frac{q}{R^2}##. The force on a...

Homework Statement Consider two solid dielectric spheres of radius ##a## separated by a dis- tance ##R## (##R\gg a##). One of the spheres has a charge ##q## and the other is neutral. We scale up the linear dimensions of the system by a factor of two. How much charge should reside on the first...

Thank you fzero! If I understand correctly, any Lorentz invariant expressions made of external momentum 4-vectors can be used as the invariant momenta and when setting the renormalization conditions at a certain scale, we just say that all those invariant momenta are of the order of magnitude of...

According to Peskin, p.414, at the bottom, as part of calculating the ##\beta## functions of a theory, we need to fix the counter terms by setting the "typical invariants" built from the external leg momenta to be of order ##−M^2##. For a 4-point function, these invariants are s, t and u...

Thanks for the reply! ##\not{\!p}^2=p_\mu \gamma^\mu p_\nu \gamma^\nu=p_\mu p_\nu(2g^{\mu\nu}-\gamma^\nu \gamma^\mu)=2p^2-\not{\!p}^2## and therefore ##p^2=\not{\!p}^2##

I am trying to calculate the ##\beta## functions of the massless pseudoscalar Yukawa theory, following Peskin & Schroeder, chapter 12.2. The Lagrangian is ##{L}=\frac{1}{2}(\partial_\mu \phi)^2-\frac{\lambda}{4!}\phi^4+\bar{\psi}(i\gamma^\mu \partial_\mu)\psi-ig\bar{\psi}\gamma^5\psi\phi.##...

Wherever I see calculations of two-loop contributions to the ##\phi^4## propagator (such as Peskin, page 328, on the bottom), only the sunset diagram (aka the Saturn diagram) is considered, but not, say, the two-loop diagram involving a loop on top of a loop (looks like this: _8_). Does it not...

Thank you! Haven't thought of going that way.

Homework Statement I'm trying to understand dimensional regularization with Peskin. There is a transitions that is not clear. Homework Equations On page 250, the general expression for the d-dimensional integral is given: ##\int \frac{d^d...

Thank you, I think I understand now. The polarization vector ##\epsilon_\mu## of the Feynman rules of QED originates from the expansion of the vector potential ##A_\mu## into creation and annihilation operators, where the vectors that appear are the basis vectors of the polarization.

Thank you for your quick answers! I still do not understand. The final photons can be in various polarization states. For example, they can be right or left circularly polarized, they can be linearly polarized along the x or y-axis or any other vector in the xy plane. So, to get the total decay...

Homework Statement I am trying to solve problem 5.4(a) in Peskin & Schroeder. I am requested to calculate the decay rate of a ##1S_0## positronium state into two photons. Obviously, we have to sum over all photon polarizations eventually to get the total decay rate. However, I do not understand...

Just noticed that the question is missing. It is to find the Lagrangian of the system.