Geodesic
Bogoliubov's metric as a~global characteristic of the~family of metrics in the~Hilbert algebra of observables
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 352-369

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

We comparatively analyze a one-parameter family of bilinear complex functionals with the sense of "deformed" Wigner–Yanase–Dyson scalar products on the Hilbert algebra of operators of physical observables. We establish that these functionals and the corresponding metrics depend on the deformation parameter and the extremal properties of the Kubo–Martin–Schwinger and Wigner–Yanase metrics in quantum statistical mechanics. We show that the Bogoliubov–Kubo–Mori metric is a global (integral) characteristic of this family. It occupies an intermediate position between the extremal metrics and has the clear physical sense of the generalized isothermal susceptibility. We consider the example for the $SU(2)$ algebra of observables in the simplest model of an ideal quantum spin paramagnet.
Keywords: operator metric, correlation function, Green's function, spectral intensity, uncertainty relation. 
@article{TMF_2009_160_2_a8,
     author = {Yu. G. Rudoi},
     title = {Bogoliubov's metric as a~global characteristic of the~family of metrics in {the~Hilbert} algebra of observables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {352--369},
     publisher = {mathdoc},
     volume = {160},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a8/}
}
TY  - JOUR
AU  - Yu. G. Rudoi
TI  - Bogoliubov's metric as a~global characteristic of the~family of metrics in the~Hilbert algebra of observables
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 352
EP  - 369
VL  - 160
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a8/
LA  - ru
ID  - TMF_2009_160_2_a8
ER  - 
%0 Journal Article
%A Yu. G. Rudoi
%T Bogoliubov's metric as a~global characteristic of the~family of metrics in the~Hilbert algebra of observables
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 352-369
%V 160
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a8/
%G ru
%F TMF_2009_160_2_a8
Yu. G. Rudoi. Bogoliubov's metric as a~global characteristic of the~family of metrics in the~Hilbert algebra of observables. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 352-369. http://geodesic.mathdoc.fr/item/TMF_2009_160_2_a8/