Geodesic
Imagery of symmetry in current physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 2, pp. 292-303
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a remarkable symmetry duality that is broken under a phase transition permitting the appearance of superconductivity and superfluidity. This is a wine-bottle rotation symmetry in a semi-phenomenological description in the spirit of Ginzburg and Landau, while it is a phase symmetry responsible for the conservation of the number of particles (helium atoms, Cooper electron pairs) in Bogoliubov's quantum theory. This duality is interesting in the context of the contraposition of logic and intuition or Science and Art. We also briefly discuss another aspect of distorted symmetry connected with varying the geometry of space–time and with dimensional reduction in particular.
Keywords: spontaneous symmetry breaking, symmetry duality, dimensional reduction
Mots-clés : phase transition, grand unification. 
@article{TMF_2012_170_2_a11,
     author = {D. V. Shirkov},
     title = {Imagery of symmetry in current physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {292--303},
     year = {2012},
     volume = {170},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a11/}
}
TY  - JOUR
AU  - D. V. Shirkov
TI  - Imagery of symmetry in current physics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 292
EP  - 303
VL  - 170
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a11/
LA  - ru
ID  - TMF_2012_170_2_a11
ER  - 
%0 Journal Article
%A D. V. Shirkov
%T Imagery of symmetry in current physics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 292-303
%V 170
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a11/
%G ru
%F TMF_2012_170_2_a11
D. V. Shirkov. Imagery of symmetry in current physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 2, pp. 292-303. http://geodesic.mathdoc.fr/item/TMF_2012_170_2_a11/

[1] L. D. Landau, ZhETF, 11 (1937), 26–47 | Zbl

[2] N. N. Bogolyubov, Izv. AN SSSR. Ser. fiz., 11:1 (1947), 77–90 ; УФН, 93:11 (1967), 552–564 | MR

[3] D. V. Shirkov, Found. Phys., 16:1 (1986), 27–38 | DOI | MR

[4] L. D. Landau, ZhETF, 11:6 (1941), 592–614; Л. Д. Ландау, УФН, 93:11 (1967), 495–520

[5] P. C. Hohenberg, P. M. Platzman, Phys. Rev. Lett., 152:1 (1966), 198–200 ; Л. Александров, B. A. Загребнов, Ж. А. Козлов, В. А. Парфенов, В. Б. Приезжев, ЖЭТФ, 68:5 (1975), 1825–1833; M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science, 269:5221 (1995), 198–201 | DOI | DOI

[6] V. L. Ginzburg, L. D. Landau, ZhETF, 20 (1950), 1064–1081

[7] L. P. Gorkov, ZhETF, 36:9 (1959), 1918–1923 | Zbl

[8] N. N. Bogolyubov, ZhETF, 34:1 (1958), 58–65 | MR | Zbl

[9] N. N. Bogolyubov, Vestn. AN SSSR, 28:4 (1958), 25–29

[10] B. A. Arbuzov, A. N. Tavkhelidze, R. N. Faustov, DAN SSSR, 139 (1961), 345–347 | Zbl

[11] D. V. Shirkov, UFN, 179 (2009), 581–589, arXiv: 0903.3194 | DOI

[12] I. Ya. Aref'eva, Phys. Lett. B, 328:3–4 (1994), 411–419, arXiv: hep-th/9306014 | DOI

[13] R. Kirschner, L. N. Lipatov, L. Szymanowski, Nucl. Phys. B, 425:3 (1994), 579–594, arXiv: hep-th/9402010 | DOI

[14] D. V. Shirkov, Pisma v EChAYa, 7:6 (2010), 625–631, arXiv: 1004.1510 | DOI

[15] P. P. Fiziev, D. V. Shirkov, TMF, 167:2 (2011), 323–336, arXiv: 1009.5309 | DOI | Zbl