I just have a very small and naive Question. In my PhD I work on different Toy models which are implemented on the lattice. In order to do so one performs a Wick rotation from minkowski to euclidean spacetime, and then basically performs all the calculations in euclidean spacetime.
I understand how the Wick rotation works and I see (mathematically), that its legit, however there is something I do not quite understand.
When working with lattice theories one always computes these quantities, e.g. particle masses (e.g. in spectroscopy) or determines scattering amplitudes etc. etc. When computing these things, it is always implied that these quantities can be understood in terms of "physical, real world quantities", despite being quantities computed in Euclidean spacetime - and not in "real world Minkowski spacetime".
My question now is the following: Is there a simple physical argument, which allows us to say that particle masses, scattering amplitudes etc. have the same physical meaning as they would have in Minkowski spacetime?
