Two particle Path Integral

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Is there such a thing as a Feynman Path Integral for two non-interacting particles? I find myself wondering how the wave function of a single particle is changed in the presence of a second particle. The Feynman path integral takes into account every possible path that a particle can take. So what would happen if there is another particle in the vicinity of the first? If both particles are only accounted for by their mass and velocity (no other forces or potentials), then how would the wave function of the first particle be changed by the mere existence of a second particle? Would the path integral of each simply ignore the existence of the other? Or would they interfere with each other in some way?
 

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Is there such a thing as a Feynman Path Integral for two non-interacting particles? I find myself wondering how the wave function of a single particle is changed in the presence of a second particle.
Normally the path integral for a free particle from a starting point to the ending point is a straight line in flat space. But if the presence of another particle interferes in some way, then I suppose the classical path would have to change to something more curved, right?
 
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