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recently I read a paper about some special tratment in QED (https://doi.org/10.1103/PhysRevLett.122.193603) and they used a lot the term "real space description" or "real space information" of photons. So my question is, what do the authors mean by that exactly?

thanks in advance

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This means the real space (position space), and not complex or momentum space.

Please see here:

https://arxiv.org/pdf/1810.09595.pdf

https://en.wikipedia.org/wiki/Position_and_momentum_space

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