Recent content by Geigercounter

Not exactly. From the equations of motion I want to find two second order differential equations in ##a(r)## and ##f(r)##. That statement is just below the relevant equations section. My apologies for the bad formatting.

The problem statement is as I've written it here. I got it from lecture notes I studied a while back when looking at solitons.

This ansatz is in the form of a soliton. In easiest case it is time independent.

Well the fields are time-independent. The hermitian conjugate of the EOM for ##\phi## is precisely the EOM for ##\phi^\dagger##. I don't see ow doing your trick in the ansatz will help further. I wrote it out but that makes everything more complicated in my opinion. What's wrong with the method...

Yes ##\psi## indeed. I'd edit the post but seems like I can't do that anymore. I don't think I'd need to rewrite in a real and imaginary part though, since I have an explicit solution (ansatz)...

I want to compute the equations of motion for this theory in terms of the functions ##f## and ##a##. My plan was to apply the Euler-Lagrange equations, but it got confusing very quickly. Am I right that we'll have 3 sets of equations? One for each of the fields ##\phi,\phi^\dagger, A_\mu## ...

@berkeman This is a different post... But I'm looking for an answer there too! If you could maybe have a look :)

The first step seems easy: computation of the $\theta$ and $\overline{\theta}$ integrals give $$Z[w] = \frac{1}{(2\pi)^{n/2}}\int d^n x \: \det(\partial_j w_i(x)) \exp{\left(-\frac{1}{2}w_i(x)w_i(x)\right)}.$$ From here, I tried using that $$\det(\partial_j w_i (x)) = \det\left(\partial_j w_i...

Yes it is! It was similar to that question but I had some extended questions and gave some more details than that thread.

First of all, I don't know where to put this. I had a thread in the advanced physics homework help (https://www.physicsforums.com/threads/calculating-the-transfer-function-for-dark-matter-numerically.1052335/#post-6883072) but it just vanished overnight. I never got a notification or something...

I'm stuggling with a similar problem! Any updates on this thread @JD_PM? or @phyzguy? I've also posted my version of this question on ths forum. I already found that the above method won't work, because this supposes an analytical solution can be found in Matlab. We'll need to implement a...