2011/04/30 by Thomas Curtright, Thomas L Curtright, Cosmas Zachos +1 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #physics.hist-ph #quant-ph
paper · pdf · doi:10.1142/s2251158x12000069
published as Asia Pacific Physics Newsletter, V1, Iss 1, May 2012, pp 37-46 · A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theory
arxiv created 2011/12/26 · openalex publication_date 2012/05/01 · arxiv updated 2012/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ever since Werner Heisenberg's 1927 paper on uncertainty, there has been considerable hesitancy in simultaneously considering positions and momenta in quantum contexts, since these are incompatible observables. But this persistent discomfort with addressing positions and momenta jointly in the quantum world is not really warranted, as was first fully appreciated 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 understood nor widely known — much less generally accepted — until the late 20th century.