The exponential of the derivative translates a function 𝑓(𝑥) by an amount εpic.twitter.com/mwQ1aLpOHt
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This is already over my head... How does that stop you knowing what's outside of your light cone? At least classically, analyticity means you would know, right?
If the operators are local operators they by definition within the light cone .. if you have local operators + Lorentz invariant lagragian you’re good to go
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But like, say they measure quantity A, which is analytic. So you measure it in a small neighbourhood of where you stand, and then you've got all its derivatives so you know the value of quantity A *everywhere* (or am I missing something because I know next to undergrad in QM)
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you're right if we're talking about pure QM .. that theory is not relativistic .. this was one of the reasons why we developed QFT
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