Path integral formulation of quantum mechanics using functional integration, due to Richard Feynman
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Functional integration, the integral of a functional over a space of curves
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The first definition was made by Meijer using a series; nowadays the accepted and more general definition is via a path integral in the complex plane, introduced in its full generality by Arthur Erdélyi in 1953.
He is known for developing the path integral formulation of the Fermionic field, inventing Grassmann integration for this purpose.
His research topics include path integral representation of Fractional Brownian motion, ring closing opening dynamics in polymers, first passage time calculation in phase space, energy transfer between molecule and graphene, quantum coherence etc.