Jonathan Gleason
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 Nov 20 awarded Custodian Nov 20 reviewed Reject Why do grapes in a microwave oven produce plasma? Nov 19 answered Density matrix: error with diagonalization claim and fixing it Nov 17 answered Is the overall force of a test charge in a electromagnetic field always the same? Nov 14 comment A question from Schwinger's particles, sources and fields monograph I am confused. In some places you write $\phi ^\mu$ and in others you write simply $\phi$. Is there a scalar field $\phi$ and a vector field $\phi ^\mu$? Nov 14 comment Calculating the Sun's emitted power in a wavelength range? See wikiwand.com/en/Stefan%E2%80%93Boltzmann_law#/… . I believe this calculation is very similar to what you would like to do. Nov 14 comment Which renormalisation techniques are available for 3+1 QED? You should probably distinguish between re-normalization and regularization. Pauli-Villars is a method of regularization. Two other ones that come to mind are dimensional regularization and the usual cut-off regularization. Nov 13 revised Where does the force to stop a constant velocity object come from? added 512 characters in body Nov 13 answered Where does the force to stop a constant velocity object come from? Nov 12 comment Momentum conservation in an electromagnetic system? Well, I honestly don't know why you would need to do this. Perhaps I misunderstand your question. I thought that you took note of the fact that momentum was not conserved, and was confused as to why that was not the case. And the reason of course is because we are applying a non-zero net force to the system. As a 'sanity check', I suppose you could actually calculate the change in momentum of those three things to verify that it does indeed come out to $f\Delta t$, but given that it's so tedious to do so, I don't know why you would want to do that. Nov 12 comment Momentum conservation in an electromagnetic system? So in particular, it shouldn't be balanced. They should differ by $f\delta t$. Also, I admittedly don't understand why you think that the momentum of the E&M field won't change unless the top charge accelerates to a non-negligible degree. The Liénardâ€“Wiechert depend on the velocity, which, for the bottom particle, is changing to a non-negligible degree (though I guess it's possible that you might find this dependence 'cancels' when you do the actual computation). Nov 12 comment Momentum conservation in an electromagnetic system? . . . Then the momentum change of the E&M field would just have to be so that, after you add these three together, you get $f\Delta t$. Nov 12 comment Momentum conservation in an electromagnetic system? So I am admittedly trying to avoid details because I believe the actual computation will be at least slightly tedious. Nevertheless, I think it's easy to see that this is possible. The system has three things contributing to its momentum: the mechanical momentum of the top particle, the mechanical momentum of the bottom particle, and the momentum of the E&M field. If we declare that the positive direction is to the right, then the momentum of the bottom particle is increasing over time and the momentum of the top particle is decreasing over time . . . Nov 12 comment Momentum conservation in an electromagnetic system? @JohnEastmond That's right. The momentum of your entire system should change (in magnitude) by $f\Delta t$ over a time period of $\Delta t$. Nov 12 answered Momentum conservation in an electromagnetic system? Nov 11 comment Why do we have to use an integral in this scenario to figure out $v_{max}$? @user42141 The kinetic energy does vary . . . $v$ depends on $r$. Nov 11 comment Why do we have to use an integral in this scenario to figure out $v_{max}$? @NeuroFuzzy Thanks for catching that. Nov 11 revised Why do we have to use an integral in this scenario to figure out $v_{max}$? added 71 characters in body Nov 11 answered Why do we have to use an integral in this scenario to figure out $v_{max}$? Nov 10 comment Derivation of the irreducible representations of SO(3) The same principle applies to both $SO(3)$ and $SU(2)$. All this essentially comes down to the trivial fact that, if $x=y$, then we must have that $f(x)=f(y)$. In $SO(3)$, the identity element and the element that rotates by $\pi$ are the same element. Hence, they must do the same thing in a representation. Obviously, this principle is still true for $SU(2)$; however, in this case, we have distinct $g,h\in SU(2)$ such that $\rho (g)=\rho (h)=1\in SO(3)$ ($\rho :SU(2)\rightarrow SO(3)$ is the map I mentioned in my answer).