Feynman Path integrals in space with holes?

[friend]

Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path integrals through a space with holes in it - with regions of space excluded from the integration process. More specifically, I'm wondering about points or regions of space where the amplitude must be zero. I assume that a point or region that is exclude from the path integral means that the amplitude will be zero there.

I've heard described elsewhere that a space with holes in it can result in a curvature of that space. And I wonder if the classical limit of a particle path will become curved due to nearby "holes". Could this result in the curvature of general relativity? A quick Google search did not result in any relevant results. So I wonder if there has been any study on this. Thanks.

 

[atyy]

Try the Aharonov-Bohm effect:
http://www.columbia.edu/~crg2133/Files/Work/termPaper.pdf
http://arxiv.org/pdf/quant-ph/0004090.pdf.

 

[friend]

Try the Aharonov-Bohm effect:

I'm not sure the Aharonov-Bohm effect is the same because the effect is due to something in a region, not due to no region. But as far as that goes, can we say that the material of the double-slit experiment (not the open slits themselves), does the material block the wave function, making the wave function of the traveling particles to be zero at the material walls? Or is there reflection or absorption that's not equivalent to the wave function being zero at the walls?