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169 views

Discretization of action in path integral

I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives: $$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right) dt ~\rightarrow~ \sum ...
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path integrals: how/why can the phase be identified with the action?

In Peskin & Schroeder, chapter 9 introduces the functional methods. The idea, to recall, is simply to sum over all the possible paths: $U(x_a,x_b;T) = \sum_{\text{all paths}} e^{i . ...