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Interpretation of Feynman's propagator

Physics Asked by MathMath on February 26, 2021

What is the interpretation of the Feynman’s propagator

$$D(x-y) :=langle 0 |phi(t,x)phi(t’,y)|0rangle~?$$

As far as I understand, it is the following. $|D(x-y)|^{2}$ is the probability density of finding a particle at state $phi(t,x)$ once it was known to be at state $phi(t’,y)|0rangle$ initially.

Moreover, in the particular case where $phi(t,x)$ is the Klein-Gordon quantum field, the interpretation of $phi(t,x)|0rangle$ is that a particle with state given by a sobreposition of well-defined momentum $|prangle$ is created at $(t,x)$. Thus, the first interpretation, in this case, reduces to "the probability density that such a particle created at $(t’,y)$ will be found in $(t,x)$".

Are my interpretations correct?

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