Phase Space

Dr. Thomas Curtright (host Ogilvie), University of Miami
December 6, 2017 at 4:00 pm
204 Crow
Event Description 

I will discuss the complete, autonomous formulation of quantum mechanics based on functions that depend simultaneously on the classical variables x and p.

Since Heisenberg’s 1927 paper on uncertainty, there has been considerable reluctance to consider positions and momenta jointly in quantum contexts, since these are incompatible observables. Indeed, Dirac had strong reservations about such an approach. Nevertheless, a discomfort to contemplate both positions and momenta simultaneously in the quantum world is not really warranted, as was first fully understood by Hilbrand Groenewold and José Moyal in the 1940s. While the formalism for quantum mechanics in phase space was wholly cast at that time, it was not completely appreciated until the late 20th century. One notable exception was provided by Richard Feynman, who contributed Negative Probability to a conference honoring David Bohm in the mid-1980s.

In this general talk I will discuss elementary features, as well as some of the early history, of this “deformation” approach to quantization. The subject is of considerable interest in various contemporary contexts.

Dr. Thomas Curtright is visiting us from the University of Miami as the Clark Way Harrison Visiting Professor in Physics at Washington University in St. Louis, September 1, 2017-December 31, 2017.

Coffee: 3:30 pm, 245 Compton