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Question for which .I feel silly asking - but since I'm still learning:

A particle state in QFT is considered to be an asymptotic state with a well defined energy. Now, if I take an ensemble of particles after a very large number of interactions (say, e.g., a macroscopic object like a person's body, and perhaps since the birth of the universe), can one say that the ensemble has a

**bounded energy?**

It would seem that the energy would have to be bounded at any time, even in an interacting picture (otherwise there would be no bound on spacetime curvature, etc., and yes, I realize I'm mixing in general relativity here). I think I'm basically asking about the spectrum of the Hamiltonian for the system - but since I'm still struggling to get through several texts, I'm unsure.

Also, given the above, there would be a maximum energy that a body could emit over a given time, correct? (If the above is correct)

Thanks!