12:30 pm Tuesday, February 15, 2011
GADGET: Feynman Diagrams for Schrodinger's Equation by Theo Johnson-Freyd (UC Berkeley) in RLM 8.136
Feynman's path integral, an important formalism for quantum mechanics, lacks a completely satisfactory analytic definition. One possible definition is as a formal power series whose coefficients are given by sums of finite-dimensional integrals indexed by Feynman diagrams. This ``formal'' path integral is used extensively in every-day physics, but is not usually compared against (mathematically rigorous, nonperturbative) quantum mechanics. In this talk, I will explain the definition of the quantum-mechanical formal path integral, and point out many of its features --- it has ultraviolet divergences unless certain compatibility conditions are met, it is coordinate-independent, it solves Schrodinger's equation --- none of which are obvious from the definitions, but rather require the combinatorics of Feynman diagrams. These results provide justification for the formal path integrals in quantum field theory. Submitted by
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