Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread.(adsbygoogle = window.adsbygoogle || []).push({});

Here's the scenario and question - consider the momentum wave function:

In general, even in a relativistic setting, one may measure an arbitrarily large momentum with some (very tiny) non-zero probability, assuming we use a wave function / wave packet formulation that allows for a solution (yes, I realize that wave functions as such are not used in QFT).

Here's what really bothers me: take QFT, and run a scattering experiment where at t = -∞ the particles going in are asymptotic free states with well-defined energies. Likewise, at t = +∞ one ends up with particles again with well defined energies, and energy is conserved. So there isnopossibility here for arbitrarily large momentums - i.e., exactly zero probability that at any point the energy can be larger than the input energy, the energy is bounded.

Now, in some sense (and please correct me if I'm wrong), the entire universe is one large scattering experiment with a fixed amount of energy. Then in no case should there ever be a situation in which the momentum wave function for a particle (or whatever this translates to in terms of field excitations in QFT) can have an arbitrarily large momentum (e.g., one should never use a Gaussian with non-zero tails if one truly want real answers... granted the Gaussian makes a great approximation if you basically ignore the tails, which is the case if I understand correctly).

Am I correct with the above? If so, what gives? Why use wave packets with non-zero tails that imply some (very small but still) non-zero probability of enormous momentums or energies, when this cannot possibly be reflected in physical reality?

Thanks.

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# I Momentum and energy in QM and QFT

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