Timeline for Fourier transform of the Coulomb potential
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2023 at 5:14 | comment | added | Luboš Motl | ...that their method doesn't work is simply a completely physically wrong, and ultimately irrational, statement by someone who is just introducing chaos and illiteracy, not adding to the knowledge of physics. The Fourier transform of the Coulomb potential is proportional to $1/q^2$, period, this is what every physicist does, a similar quantity appears in all basic propagators in quantum field theory etc. There are additional subtleties like the i epsilon in the denominator that a physicist has to understand and use. Who has psychological obstacles, cannot become a particle physics. Period. | |
| Feb 12, 2023 at 5:12 | comment | added | Luboš Motl | The Fourier transform of fields in 3D space or 4D spacetime, especially the flat one, is a superbly important and omnipresent tool that is used and may be used everywhere by physicists who actually understand their field. This also means that they have no problem with the treatment of the Coulomb potential which is one of the most elementary functions of space that appears in field theory. So they damn know what they determine to be the Fourier transform of the Coulomb potential and claiming that the transform doesn't exist or physicists should admit that their method... | |
| Feb 12, 2023 at 5:10 | comment | added | Luboš Motl | Physics is not about philosophers' incoherent essays what "exists" which have no operational meaning. The Fourier transform exists in the mathematical sense. A physically unreal model may also exist in the mathematical sense and in more experimental situations, we use a more tangible meaning of "existing", like the existence in a given region and a given period of time, as a property of a particular physical system. At any rate, I think it is crazy to evolve a particular technical question towards similar vacuous philosophical babbling. | |
| Feb 10, 2023 at 19:57 | comment | added | Jbag1212 | The Coulomb potential may certainly exist, but this doesn't seem to imply that the Fourier transform, a mathematical object, must exist. One could certainly conceive of a variety of physical things which certainly exist, but some corresponding mathematical transformation of that thing doesn't exist. For example: a nonconservative force field does not have a "potential". | |
| Mar 25, 2011 at 16:43 | comment | added | Vladimir Kalitvianski | Once I encountered a problem with divergent matrix elements so the perturbation theory series were useless whereas the problem had clearly physical and mathematical finite solution and their power expansions. I had a very strong temptation to discard divergent parts in the matrix elements. Fortunately, I found the true reason of their divergence and a way to reformulate the problem without this difficulty. This taught me that sometimes divergent results may be correct. | |
| Mar 24, 2011 at 20:15 | comment | added | genneth | That reminds me of a lecturer I had: "this series obvious converges because it's physical". I went through multiple cycles of utter belief and disbelief in a few minutes thinking about that one. | |
| Mar 23, 2011 at 18:30 | history | answered | Luboš Motl | CC BY-SA 2.5 |