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This article is cited in 4 scientific papers (total in 4 papers)
Bogoliubov's metric as a global characteristic of the family of metrics in the Hilbert algebra of observables
Yu. G. Rudoi Peoples' Friendship University of Russia, Moscow, Russia
Abstract:
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.
Received: 20.08.2009
Citation:
Yu. G. Rudoi, “Bogoliubov's metric as a global characteristic of the family of metrics in the Hilbert algebra of observables”, TMF, 160:2 (2009), 352–369; Theoret. and Math. Phys., 160:2 (2009), 1161–1176
Linking options:
https://www.mathnet.ru/eng/tmf6403https://doi.org/10.4213/tmf6403 https://www.mathnet.ru/eng/tmf/v160/i2/p352
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Abstract page: | 413 | Full-text PDF : | 199 | References: | 61 | First page: | 6 |
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