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...
Homework Statement
Why does the symmetry ##\phi\rightarrow-\phi## mean that an amplitude can be written as
##\alpha + \beta p^2 + \gamma p^4 + ...##
without the odd terms in ##p##?
Homework Equations
I understand that, due to this symmetry, any diagram in ##\phi^4## has an even number of...
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...