# What actually led Feynman to the path integral formulation of quantum mechanics?

It is commonly known that Feynman's path integral was inspired by Dirac's observation that the kernel is proportional to $$\exp{iS/\hbar}$$. It was Feynman, however, who had the idea of expressing the kernel as the integral of such an expression over all possible paths.

Is it known what led Feynman to try out this idea of an integral over all paths? He provides motivation from a probabilistic understanding of quantum mechanics in "Non-relativistic Quantum Mechanics" and Quantum Mechanics and Path Integrals, but is this motivation what actually led him to try out the idea of the path integral and discover that up to suitable normalization, it recovered the correct expression for the kernel and the Schrodinger equation?

Moreover, why was Dirac's observation of the proportionality of the final answer to $$\exp{iS/\hbar}$$ insufficient as the basis for an alternative formulation of quantum mechanics.

• Feynman was certainly inspired by the variational principles of classical mechanics. Apr 13 '19 at 23:03

It was Dirac's paper The Lagrangian in Quantum Mechanics. He gave more than just a remark about $$\exp{iS/\hbar}$$, he described the general structure of the path integral expression for the transition amplitude, see Dirac's remark that inspired Feynman when formulating path integral on Physics SE. But he did not come up with the suggestive intuition of summing over paths, or developed a computational procedure that could be followed, or related it to the semi-classical approximation. Fortunately, Dirac was pretty explicit as to what motivated him: