Say you have some arbitrary distribution of 4-current density and Faraday tensor in Minkowski space, which satisfies Maxwell's equations and the Lorentz force law. Has it ever been found worthwhile to Wick rotate such a problem to 4D Euclidean space in order to solve it, and if so, do any interesting features crop up upon doing so? Like, do charges behave in a qualitatively different manner in Euclidean space? I was wondering because I thought Wick rotation was only important for quantum theory, but then I saw the example here that shows it can be useful in classical physics too.
Asked
Active
Viewed 104 times
0
-
Possible duplicate: How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)? – Qmechanic Mar 15 '23 at 16:40
-
EM waves won't be waves anymore. – Kurt G. Mar 15 '23 at 16:43
-
@KurtG. Oh wow, that is interesting. So the fields would essentially solve the 4D Laplace equation rather than the wave equation...which totally makes sense, because the wave operator/d'Alembertian is really the Minkowski version of the Laplacian. I wonder then, how would the frequency of the Minkowski EM wave manifest in Euclidean space? What aspect of the solution would it correspond to? – Adam Herbst Mar 16 '23 at 02:46
-
@AdamHerbst perhaps your question is a chance for me to underdstand what Wick rotation really is about. I am not a professional physicist. Another example where it completely changes the physics is the Feynmann path integral. Feynman's version solves proplems in QFT. Mark Kac's Wick rotated version has not even anything to do with QM. Instead with the heat equation. – Kurt G. Mar 16 '23 at 05:21
-
You can simply see this at the two PDEs ( Schrödinger / heat ) themselves. – Kurt G. Mar 16 '23 at 05:29
-
@KurtG. Very interesting, thanks for the input. – Adam Herbst Mar 16 '23 at 06:51