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The way how Zwiebach was using the proper time [tex]\tau[/tex] seemed dangerous. It's ratio to the time [tex]t=x^0[/tex] depends on the particle's velocity. So if you in quantum mechanics parametrize the wave function with such proper time, [tex]\psi(x,\tau)[/tex], aren't you having different fourier amplitudes propagating with "different speeds in time" then? It looks very messy. I have difficulty seeing what's happening with that kind of approach.

Zwiebach seemed to be mainly interested in the operators. There was no discussion about spatial probability densities. Am I wrong to guess that despite the fact that string theorists have a technique to quantize a relativistic point particle, they have nothing to say about the probability densities of relativistic particles?