Is quantum field theory really lorentz invariant?

[arkajad]

By the way, thanks for not writing my name as "Nicolic", which for some reason many people do. :-)

Sorry for that. I know the pain.

 

[Demystifier]

By the way, if you write "Nicolic" in the google, the first thing it writes is:
"Did you mean: Nikolic"

 

[pellman]

Specifically, at low energies it appears as if the wavefunction on 4n dimensional configuration space has a nonzero value only when the time coordinates for all the particles are equal, and I'm still not clear how that mathematically arises.

Well, whatever it is, it must be the case that in the limit for c goes to infinity (or small energies) the wave function for a single particle system satisfies

$$\frac{\partial}{\partial t}\int{|\psi(x,t)|^2 d^3x}\rightarrow 0$$

so that we can normalize the integral over space and use the wave-function-squared as a probability density at each time t, so that time reduces to a parameter.

For multiple particles, you would have to express the wave-function in a many-time formulation, as Demystifier says, so that the wave-function would represent the probability amplitude of observing the first particle at x1,t1, the second particle at x2,t2, etc. The non-relativistic limit would be letting c go to infinity and setting t1 = t2 = ... = tn = t. But the wave-function is not necessarily zero if the times are unequal. It's just that you can only restore the usual time-parametrized Schrödinger picture by setting them equal.

I'm glossing over some fine points, but that is essence of it .