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1. ### Virtual particle propagators in QFT

Yes, I was also thinking about something along these lines. Thanks.
2. ### Virtual particle propagators in QFT

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...
3. ### Integrating a Vector Field Over a Circular Disk

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?
4. ### How to solve this nonlinear ODE?

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...
5. ### How to solve this nonlinear ODE?

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 +...