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### Where is the Feynman Green's function in quantum mechanics?

In quantum field theory, the Feynman/time ordered Green's function takes the form $$D_F(p) \sim \frac{1}{p^2 - m^2 + i \epsilon}$$ and the $i \epsilon$ reflects the fact that the Green's function is ...
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### Causal propagator and Feynman propagator

I have some questions about the Green’s function of the Klein-Gordon operator and the Feynman propagator. The first is about retarded Green’s function: \begin{eqnarray} \int_{-\infty}^\infty\frac{d^...
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### Green functions, Propagators and probability amplitude that a particle propagates

(The original post has been copiously edited to make it more clear but it still precisely corresponds to what I had intended to ask) My QFT knowledge has very much rusted and i got confused by these ...
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### Are propagators in QFT really Green functions?

In many textbooks the notions Green function and propagator are used interchangeably. But are they really the same thing? This popular answer argues that a retarded propagator function \$D_R(x,t,x',t')...
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### Definition of vacua in QFT in generic spacetimes

I have been learning QFT in curved spaces from various sources (Birrell/Davies, Tom/Parker, some papers), and one thing that confuses me the most is the choice of vacua in various spacetimes, and the ...
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Define a single-particle Green's function as $$i\hbar G(xt;x't') = \langle x| e^{-iH(t-t')/\hbar} | x'\rangle.$$ By inserting the completeness relation, we have \begin{...