Recent content by Matthaeus

Yes, I was also thinking about something along these lines. Thanks.

I am reading a nice book (Quarks and Leptons, by Halzen and Martin) about particle physics. It states that the general form of the propagator of a virtual particle is: \dfrac{i\sum_{\text{spins}}}{p^2 - m^2} I see that this is the case for the Dirac propagator...

Can you explain some details? Where does the integral come from? Are v and omega constant for all r? Is omega perpendicular to the disk?

I assumed you were familiar with the definition of first integral. A first integral for the system y' = g(y), g : D \subseteq \mathbb{R}^n \rightarrow \mathbb{R}^n is a C^1 scalar function E : D \rightarrow \mathbb{R} constant on every solution of the system. In other words, if \phi : I...

Your equation is equivalent to a first-order system, if we let F = u and F' = v: \begin{cases}\dot{u} = v \\ \dot{v} = ku-v^2\end{cases} From there you can quite easily find a first integral and then separate variables in the second equation: \begin{cases}\dot{u} = v \\ \dot{v}^2 = v^4 +...