Feynman propagator and particle uniqueness

[johne1618]

In his layman's guide to QED Feynman defines a particle propagator as a function that gives you the amplitude that a particle, that was initially at spacetime event $x$, will be found at spacetime event $y$.

But does this definition assume that the particle is unique so that if you find it at the spatial coordinates of $y$ then you are automatically guaranteed that it is no longer at the spatial coordinates of $x$?

As particles are indistinguishable maybe the propagator only specifies the amplitude that, given a particle is at event $x$, then an *additional* particle of the same type will be found at $y$.

In that case maybe one also needs to apply a reverse propagator that gives the amplitude that an antiparticle will be found at $x$ given that a particle was found at $y$?

Perhaps this would destroy the original particle at $x$ and so ensure that we are only left with a particle at $y$.

Does this make sense?

 

[ShayanJ]

The introductory quantum mechanics is a single particle theory.I urge you to check that Feynman is talking about a single-particle problem or not.Things get different where the number of particles gets bigger than one.

 

[tom.stoer]

The propagator does not act on a particle, but on a field. The amplitude you are talking about is related to this field. The particle interpretation is not based on propagators.