I'm starting to dive into the Path Integral formulation and this is taking me to turn things upside-down from what I thought of the order of what relies on what

I'm starting to dive into the Path Integral formulation and this is taking me to turn things upside-down from what I thought of the order of what relies on what. I've started to get Baez's view [1] and given that, the question in [2] becames more and more important. But it's never too late to learn. An important element is to search the simplest cases posible, discrete better than continuous, finite beter than countable. If you think of a matrix as a number-labeled bipartite graph, and you glue the graphs of a sequence of matrices the only sensible way, then the product of the sequence is a "path sumatorial", look at here [3]. You sum productorials one for each path, the sum extending to all paths. That is readable in the original Feynman paper. That is for finite state spaces. For a continous state space (e. g. some real variables), the integral became a path integral, and you are integrating a functional over paths, so you need a Lebesgue measure on a space of paths to do a Lebesgue Integral. Baez has some old lectures that develop further. [1] https://www.classe.cornell.edu/spr/1999-03/msg0015539.html https://www.classe.cornell.edu/spr/1999-03/msg0015539.html [2] https://hsm.stackexchange.com/questions/553/why-isnt-feynmans-path-integral-taught-more-widely-and-earlier-in-todays-acad https://hsm.stackexchange.com/questions/553/why-isnt-feynman... [3] https://www.math3ma.com/blog/matrices-probability-graphs https://www.math3ma.com/blog/matrices-probability-graphs