# Propagator from a spacetime point to itself and physical interpretation of vacuum

I am following a lecture note on the QFT.

But am a little confused about some parts related to the vacuum bubbles.

We define the Feynman propagator, $$D_{F}(x-y)$$, as giving the amplitude for a particle emitted at $$x$$ to propagate to $$y$$ (where it can be measured).

After following the LSZ reduction formalism and Wick's theorem we arrive at the Feynman Diagrams.

At first order we see disconnected diagrams. Here we deal with terms like $$D_{F}(z_{1}-z_{1})D_{F}(z_{1}-z_{1})$$ and also $$D_{F}(z_{1}-z_{2})D_{F}(z_{2}-z_{1})$$, etc.

And here is my question: what could be the physical interpretation of this term: $$D_{F}(z_{1}-z_{1})$$.

Based on the definition above, the term reads as the amplitude of a particle emitted at $$z_{1}$$ to propagate to the same point in space-time.

I see that when we write $$D_{F}(z_{1}-z_{2})$$, for two different points in vacuum, we can still say that such a particle is propagated. And if this was part of a fully connected Feynman diagram we interpret it physically as a virtual particle (off-shell) exchanged or propagated.

But a one-loop vacuum bubble $$D_{F}(z_{1}-z_{1})$$ or a double-loop vacuum bubble $$D_{F}(z_{1}-z_{1})D_{F}(z_{1}-z_{1})$$ doesn't make an intuitive physical sense, in particular, what propagation from $$z_{1}$$ to $$z_{1}$$ would mean here in space-time?

• – aitfel Nov 15 '20 at 16:22