Recent content by andert

Take this special case though: I'm only interested in the cases where a>0, b>0, c real, and d< 0. There should be (by Descartes rule of signs) two real solutions. When I plot the graph, the solutions of the quartic appear to converge to the quadratic solutions. So it appears that my recursion...

Yes, I just thought of that too. The quartic solution x would be proportional to 1/a^(1/4) unfortunately, so that term would not be "small" after all.

I want to solve a depressed quartic: ax^4 + bx^2 + cx + d = 0 Assume |a|\ll |b|,|c|,|d|. I would like to find the solutions by expanding around the solution to the quadratic. If you try to solve in, say, Maple, and expand around a in a series you get something that blows up. That seems silly...

I have been reading about this lately. It's quite interesting. The process is not fusion at all, but purely a weak force interaction. The 2004 DOE review of LENR certainly supported the idea that no strong force interactions were taking place. The theory has been gaining ground lately. I think...

The index for SU(3) should be 3 in the adjoint representaion (and N generally). You should probably ask him to clarify.

Right, the on mass shell concept becomes more visible when doing Feynman diagrams where you see the, e.g., scalar field propagator of the Klein-Gordon action: D(x,y) = \frac{1}{(2\pi)^4}\int d^4k \frac{e^{-ik(x-y)}}{k^2 - m^2 \pm i\epsilon} which gives the probability amplitude for a...

Check out the thread on "Neutronium armor". Sorry, can't post links yet.

In particular, say A(C,\epsilon) is the "surface area". Then we can expand it: A(C,\epsilon) = A(C,0) + \epsilon (dA/d\epsilon)(C,0) + \dots How do I figure out what (d^nA/d\epsilon^n)(C,0) is from the equation for the level set?

Is anyone familiar with books or papers on perturbation theory for closed levels sets in which the equation for the n-sphere is perturbed? For example, the level set: \sum_{i=1}^n x_i^2 + \epsilon p(x_i) = C where \epsilon is a small parameter and p(x_i) is a positive polynomial such as x_i^4.

Alright, yes, coordinate system or gauge. I see that. Each of them is a in a specific gauge. Now, what is different about the gauges of the 1PN and Schwarzschild metrics specifically? The 1PN gauge is a harmonic one. So if I were to take a static spherically symmetric field, I would have...

I'm sure there is a simple answer to this question, but I have been looking at the first Post-Newtonian (1PN) metric (for my own research) and noticed that the time-time component of the GR metric is: g_{00} = -1 + 2U - 2 U^2 where U is the Newtonian potential. The time-time component...

My preferred way to think of momentum is as part of the stress-energy-momentum tensor which is a covariance matrix that becomes diagonal (assuming an orthogonal coordinate system) when the observer and the object are at rest with respect to one another. Momentum forms the time-space components...