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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf9378https://doi.org/10.4213/tmf9378 https://www.mathnet.ru/eng/tmf/v194/i2/p187
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Abstract page: | 447 | Full-text PDF : | 130 | References: | 55 | First page: | 20 |
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