Geodesic
Bogoliubov quasiaverages: Spontaneous symmetry breaking and the~algebra of fluctuations
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 187-223

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

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. 
@article{TMF_2018_194_2_a0,
     author = {W. F. Wreszinski and V. A. Zagrebnov},
     title = {Bogoliubov quasiaverages: {Spontaneous} symmetry breaking and the~algebra of fluctuations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {187--223},
     publisher = {mathdoc},
     volume = {194},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a0/}
}
TY  - JOUR
AU  - W. F. Wreszinski
AU  - V. A. Zagrebnov
TI  - Bogoliubov quasiaverages: Spontaneous symmetry breaking and the~algebra of fluctuations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 187
EP  - 223
VL  - 194
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a0/
LA  - ru
ID  - TMF_2018_194_2_a0
ER  - 
%0 Journal Article
%A W. F. Wreszinski
%A V. A. Zagrebnov
%T Bogoliubov quasiaverages: Spontaneous symmetry breaking and the~algebra of fluctuations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 187-223
%V 194
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a0/
%G ru
%F TMF_2018_194_2_a0
W. F. Wreszinski; V. A. Zagrebnov. Bogoliubov quasiaverages: Spontaneous symmetry breaking and the~algebra of fluctuations. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 2, pp. 187-223. http://geodesic.mathdoc.fr/item/TMF_2018_194_2_a0/