I am trying to understand the relation between properties and the particle number operator. How does the particle number operator connect to properties like mass, charge, color, spin? Are those properties observables? Coordinates? Bases?

This question seems to say there might not be any number operators in QFT Number operator in interacting quantum field theory.

  • $\begingroup$ Could you try to clarify your question? I'm struggling to understand it. $\endgroup$
    – innisfree
    Apr 6, 2018 at 1:10
  • 1
    $\begingroup$ In some theories a thing called a particle has properties like mass from the offset. In QFT it seems there might not even be particles. I wonder what the connection between particle numbers (the closest thing to particles I have found) and mass, charge etc is in this context. Is mass a functional? Is mass an observable? Is mass a basis in a hilbert space? ... $\endgroup$
    – Emil
    Apr 6, 2018 at 5:34
  • $\begingroup$ Given a state, you can compute its energy and momentum and hence its invariant mass. Is there anything else you were looking for? $\endgroup$
    – knzhou
    Apr 19, 2018 at 9:27


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