T. Curtright, and C. Zachos. (2011)cite arxiv:1104.5269Comment: A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theory.
DOI: 10.1142/S2251158X12000069
Abstract
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.
%0 Generic
%1 curtright2011quantum
%A Curtright, Thomas L
%A Zachos, Cosmas K
%D 2011
%K mechanics phase quantum space
%R 10.1142/S2251158X12000069
%T Quantum Mechanics in Phase Space
%U http://arxiv.org/abs/1104.5269
%X 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.
@misc{curtright2011quantum,
abstract = {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 Jos\'e 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.},
added-at = {2013-12-23T11:51:50.000+0100},
author = {Curtright, Thomas L and Zachos, Cosmas K},
biburl = {https://www.bibsonomy.org/bibtex/201f056fa0d833ceb98359bc466ec7287/aeu_research},
description = {Quantum Mechanics in Phase Space},
doi = {10.1142/S2251158X12000069},
interhash = {2dc7d9a8228bfc8b04da1a60b4a07ab7},
intrahash = {01f056fa0d833ceb98359bc466ec7287},
keywords = {mechanics phase quantum space},
note = {cite arxiv:1104.5269Comment: A brief history of deformation quantization, ca 1930-1960, with some elementary illustrations of the theory},
timestamp = {2013-12-23T11:51:50.000+0100},
title = {Quantum Mechanics in Phase Space},
url = {http://arxiv.org/abs/1104.5269},
year = 2011
}