Why is it that, in the definition of the path integral, we have the(adsbygoogle = window.adsbygoogle || []).push({}); of neighboring integrals of the form : ∫Φdxproduct_{1}.....dx_{n}when the whole idea is based on adding the contribution of neighboring paths. I need some help understanding why it is of the form ∫Φdx_{1}.....dx_{n}and not the form ∫Φdx_{1}+∫Φdx_{2}+...∫Φdx_{n}where Φ is e^{iS/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 ∫Φdx_{i}and we add each contribution in the discrete limit Σ∫Φdx_{i}. Why is it that this turns into a chain of differentials dx_{i}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.

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# Definition of the Path Integral

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