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$\mathrm{i}\epsilon$ prescription makes a function analytical?
I've seen this everywhere where they say "Analytic continuation is obtained by the usual $\mathrm{i}\epsilon$ prescription..." but how is that?
How do you analytically continue (say) $\ln x$ with ...
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Analytic continuation of imaginary time Greens function in the time domain
Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature
$$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$
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