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Jun
22
comment Energy efficiency of antimatter producion
Also, even if you could get antimatter stored in considerable quantities, with efficiency close to 1 (not bigger). What would you do with it? Eletron-positron pairs anihilate into 500 keV gamma rays, which is very bad for propulsion. Photons this hard can´t just be reflected for push. You would have to find materials that would absorb and thermalize them, and then eject these. I don't think this is much better than what we already do, at much higher costs.
Jun
22
accepted Imaginary pertubation to a Hamiltonian: how is it the same as rotation to imaginary time?
Jun
21
comment Imaginary pertubation to a Hamiltonian: how is it the same as rotation to imaginary time?
(...) he uses exactly this substitution to get $Z[J]$. Of course, the potential for a free scalar field is proportional to $q^2$, but wouldn't adding the whole $i\epsilon H$ mess up the momentum integral you need to get from the hamiltonian to the lagrangean? The bothering point here is that this $i \epsilon$ factor will be the one (on page 185) dictating the path of integration to get the propagator.
Jun
21
comment Imaginary pertubation to a Hamiltonian: how is it the same as rotation to imaginary time?
Yes, I noticed it would be far simpler to add $i \epsilon H$ but, when the author goes on to quantizing a scalar field (page 182)
Jun
21
awarded  Critic
Jun
21
accepted What is the relation between (physicists) functional derivatives and Fréchet derivatives
Jun
20
asked Imaginary pertubation to a Hamiltonian: how is it the same as rotation to imaginary time?
Jun
19
comment What is the relation between (physicists) functional derivatives and Fréchet derivatives
That´s exactly my problem with this definition (Dirac delta subtleties apart). It seems your are defining the partial derivative in the specific direction of $\delta_y$, but this very definition is used everywhere as the partial derivative in any direction (are they all the same?). Another way of expressing my problem: is the first equality below valid? Why? (I tried to follow your notation, $f_y$ means f calculated at point $y$): $$ \frac{\delta F}{\delta (f_y)}[f] = \frac{\delta F}{\delta (\delta_y)}[f] = \lim_{\epsilon \to 0} \frac{1}{\epsilon} ( F[f + \epsilon \delta_y] - F[f]). $$
Jun
19
awarded  Editor
Jun
19
revised What is the relation between (physicists) functional derivatives and Fréchet derivatives
Corrected Spelling
Jun
19
awarded  Supporter
Jun
19
answered Why does paper become transparent when smeared with oil but not (so much) with water?
Jun
19
awarded  Teacher
Jun
19
answered Why is paper more frangible when it is wet?
Jun
18
asked What is the relation between (physicists) functional derivatives and Fréchet derivatives
Jan
21
awarded  Student
Jan
21
awarded  Scholar
Jan
21
accepted Understanding boundary conditions on slices of AdS5
Jan
21
asked Understanding boundary conditions on slices of AdS5