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accepted Propagator for Dirac equation in real space
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answered Propagator for Dirac equation in real space
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comment Propagator for Dirac equation in real space
@Trimok: Moving the differentiation under the integral sign would mean that the propagator involves the derivative of a delta function, though, which I find odd. You make the argument that you "involving a derivative" is not an invariant property of the propagator, which I can't deny. One way to formalize it is to ask whether the solution changes when we add a constant to the function $f \to f + C$. (But this may be forbidden due to boundary conditions.)
Oct
25
comment Propagator for Dirac equation in real space
I understand that, what I'm looking for is an explicit formula for the Greens function $G_1(x,x;t,t')$. I have the impression that it involves the derivative of a $\delta$-function, and I just want to make sure that this is correct by comparing to an explicit reference. (All textbooks that I've looked at only calculate the Fourier transform $G_1(k;t,t')$).
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comment Propagator for Dirac equation in real space
@Trimok: We can choose $f(x',t') = g(x')\delta(t'-t_0)$ to model initial conditions at a time $t_0$. In general, the propagator for a driving force $f$ can always be used to construct the propagator for initial conditions $ψ(x,t_0)$.
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asked Propagator for Dirac equation in real space
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