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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 2, Pages 352–369
DOI: https://doi.org/10.4213/tmf6403
(Mi tmf6403)
 

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
Full-text PDF (551 kB) Citations (4)
References:
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
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 2, Pages 1161–1176
DOI: https://doi.org/10.1007/s11232-009-0108-1
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\crossref{https://doi.org/10.1007/s11232-009-0108-1}
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  • https://doi.org/10.4213/tmf6403
  • https://www.mathnet.ru/eng/tmf/v160/i2/p352
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:413
    Full-text PDF :199
    References:61
    First page:6
     
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