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A single point in quantum configuration space, is the product of multiple point positions per quantum field ...

An attempt at translation: each point in the quantum configuration space corresponds to a particular configuration of every field (e.g. electromagnetic, gluon, electron etc.), and the regularities in these fields tell us how many particles of each species do we have and where they are. Is this even approximately correct?

So... how many dimensions does the real quantum configuration space then have? Uncountably infinite?

In quantum physics, the configuration space is the fundamental thing, and you get the appearance of an individual particle when the amplitude distribution factorizes...

Um, if individual particles are derived from the amplitude distribution on the configuration space, and the dimension of that space is related to the number of those particles, how do we then know how many dimensions should a particular configuration space have?

Concretely, how did we know that we have to draw a 2-d diagram (+2 dimensions for the amplitudes) up there? One spatial dimension for each photon? Ok, but supposedly we don't know how many photons are there - actually, individual photons don't even exist fundamentaly - since this should be a derived fact from the amplitude distribution, right? Do we just guess and see which picture comes out as the most natural?

It all seems kind of circular... in a confused corner of my mind at least - help, please? :-/