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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 194, Number 2, Pages 187–223
DOI: https://doi.org/10.4213/tmf9378
(Mi tmf9378)
 

This article is cited in 6 scientific papers (total in 6 papers)

Bogoliubov quasiaverages: Spontaneous symmetry breaking and the algebra of fluctuations

W. F. Wreszinskia, V. A. Zagrebnovbc

a Instituto de Física, Universidade de São Paulo, São Paulo, Brazil
b Département de Mathématiques,d'Aix-Marseille Université, Marseille, France
c Institut de Mathématiques de Marseille, Marseille, France
Full-text PDF (789 kB) Citations (6)
References:
Abstract: We present arguments supporting the use of the Bogoliubov method of quasiaverages for quantum systems. First, we elucidate how it can be used to study phase transitions with spontaneous symmetry breaking (SSB). For this, we consider the example of Bose–Einstein condensation in continuous systems. Analysis of different types of generalized condensations shows that the only physically reliable quantities are those defined by Bogoliubov quasiaverages. In this connection, we also solve the Lieb–Seiringer–Yngvason problem. Second, using the scaled Bogoliubov method of quasiaverages and considering the example of a structural quantum phase transition, we examine a relation between SSB and critical quantum fluctuations. We show that the quasiaverages again provide a tool suitable for describing the algebra of critical quantum fluctuation operators in both the commutative and noncommutative cases.
Keywords: quasiaverages, generalized condensation, critical quantum fluctuations.
Received: 01.04.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 194, Issue 2, Pages 157–188
DOI: https://doi.org/10.1134/S0040577918020010
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: W. F. Wreszinski, V. A. Zagrebnov, “Bogoliubov quasiaverages: Spontaneous symmetry breaking and the algebra of fluctuations”, TMF, 194:2 (2018), 187–223; Theoret. and Math. Phys., 194:2 (2018), 157–188
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9378
  • https://doi.org/10.4213/tmf9378
  • https://www.mathnet.ru/eng/tmf/v194/i2/p187
  • This publication is cited in the following 6 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:447
    Full-text PDF :130
    References:55
    First page:20
     
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