Geodesic
Geometrization of quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 20-31

Voir la notice de l'article provenant de la source Math-Net.Ru

We show that various descriptions of quantum mechanics can be represented in geometric terms. In particular, starting with the space of observables and using the momentum map associated with the unitary group, we give a unified geometric description of the different pictures of quantum mechanics. This construction is an alternative to the usual GNS construction for pure states.
Keywords: quantum mechanics, Hermitian structure, Jordan algebra
Mots-clés : Poisson bracket, Lie–Jordan algebra. 
@article{TMF_2007_152_1_a1,
     author = {J. F. Carinena and J. Clemente-Gallardo and G. Marmo},
     title = {Geometrization of quantum mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {20--31},
     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a1/}
}
TY  - JOUR
AU  - J. F. Carinena
AU  - J. Clemente-Gallardo
AU  - G. Marmo
TI  - Geometrization of quantum mechanics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 20
EP  - 31
VL  - 152
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a1/
LA  - ru
ID  - TMF_2007_152_1_a1
ER  - 
%0 Journal Article
%A J. F. Carinena
%A J. Clemente-Gallardo
%A G. Marmo
%T Geometrization of quantum mechanics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 20-31
%V 152
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a1/
%G ru
%F TMF_2007_152_1_a1
J. F. Carinena; J. Clemente-Gallardo; G. Marmo. Geometrization of quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 20-31. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a1/