Andre dinu: The state of a system with variable number of identical particles is described by a vector in fox space, which is the direct sum of several hilbert spaces. When you excite the field just enough to have exactly one particle, and that particle can be doing different things. So whenever you have a situation where particles are created or destroyed through interactions, field theory is a way to sort of summarize what's going on there.
Welcome to the March 2022 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questions asked by Patreons, whittle them down to a more manageable size — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!
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