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I am reading QFT by Lancaster and Blundell. In chapter 4 of the book the field operators are introduced:

"Now, by making appropriate linear combinations of operators, specifically using Fourier sums, we can construct operators, called field operators, that create and annihilate particles, but this time they don’t create/annihilate particles in particular momentum states but instead they create/annihilate particles localized at particular spatial locations. Thus the operator defined by

ψ^{†}(x)=I/√ν Σ_{p}a^{†}_{p}e^{-ip.x}"

Won't this violate the uncertainty principle? I thought maybe it just creates the particle, after which the particle obeys the relation, but in the very next example(4.1) they go ahead to find the position and momentum of the particle(which they do accurately it seems?). What am I missing here?

Thank you for your time

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# I Field operators and the uncertainty principle

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