Why is it that, in the definition of the path integral, we have the product of neighboring integrals of the form : ∫Φdx1.....dxn when the whole idea is based on adding the contribution of neighboring paths. I need some help understanding why it is of the form ∫Φdx1.....dxn and not the form ∫Φdx1+∫Φdx2+...∫Φdxn where Φ is eiS/ħ. I hope I'm making sense. In the formulation of the idea, we have discrete points in time where we sum over all values of x at that point, namely ∫Φdxi and we add each contribution in the discrete limit Σ∫Φdxi. Why is it that this turns into a chain of differentials dxi in the limit that the length of the time intervals goes to 0 and the number of intervals goes to infinity? Again, I hope this makes sense and that you can shed some light on this for me.