**Thursday, May 17**

Mathematical Challenges of Feynman's Path Integral

**Arlo Caine **

Cal Poly Pomona

In a flash of characteristically creative insight, Richard Feynman introduced a formalism for computing the probability amplitude for a particle to transition between two positions in terms of an integral over the space of all possible paths between those positions. The beauty of this formalism is that the path of the particle predicted by classical mechanics evidently contributes the most to this sum and hence the formalism provides a conceptual link between quantum and classical mechanics. For this reason, the path integral technique is employed in almost all branches of modern theoretical physics. Although powerful and effective (the formalism makes possible the impressively accurate calculations of QED for example) it has not been successfully made sense of as a mathematical object. In this talk, I will showcase Feynman's brilliant derivation in the context of 1D quantum mechanics, highlighting the mathematical difficulties, and summarize the efforts to make precise sense of this beautiful theoretical tool.

Refreshments at 10:50 AM. Seminar begins at 11:00 AM.

Building 8, Room 241

For further information, please call (909) 869-4014