Geodesic
Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 320-331 
A. N. Vasil'ev. Consequences of the convexity of Legendre transformations (generalized Goldstone theorem). Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 320-331. http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a4/
@article{TMF_1973_15_3_a4,
     author = {A. N. Vasil'ev},
     title = {Consequences of the convexity of {Legendre} transformations (generalized {Goldstone} theorem)},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {320--331},
     year = {1973},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a4/}
}
TY  - JOUR
AU  - A. N. Vasil'ev
TI  - Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 320
EP  - 331
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a4/
LA  - ru
ID  - TMF_1973_15_3_a4
ER  - 
%0 Journal Article
%A A. N. Vasil'ev
%T Consequences of the convexity of Legendre transformations (generalized Goldstone theorem)
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 320-331
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a4/
%G ru
%F TMF_1973_15_3_a4

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

Some consequences of the already proven convexity of Legendre transformations are analyzed. Different possible behaviors of a system are considered; in particular, degeneracy and a phase transition. A generalization of Goldstone's theorem [1, 2] is proved: in every theory with continuous degeneracy of the solution, zero-mass particles are present. Spontaneous breaking of continuous symmetry automatically leads to Continuous degeneracy, which explains why zero-mass particles arise in theories with broken symmetry.

[1] J. Goldstone, Nuovo Cim., 19 (1961), 154 | DOI | MR | Zbl

[2] J. Goldstone, A. Salam, S. Weinberg, Phys. Rev., 127 (1962), 965 | DOI | MR | Zbl

[3] C. de Dominicis, P. C. Martin, J. Math. Phys., 5, 14 ; (1964), 31 | DOI | DOI

[4] J. Schwinger, Proc. Nat. Acad. Sci., 37 (1951), 452 | DOI | MR | Zbl

[5] E. S. Fradkin, Dissertatsiya, Tr. FIAN, 29 (1965), 7 | Zbl

[6] G. Jona-Lasinio, Nuovo Cim., 34 (1964), 1790 | DOI

[7] H. D. Dahmen, G. Jona-Lasinio, Nuovo Cim., 52A (1967), 807 ; 62A (1969), 889 | DOI | DOI

[8] R. P. Feynman, Rev. Mod. Phys., 20 (1947), 376 | MR

[9] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Gostekhizdat, 1957 | MR

[10] P. W. Higgs, Phys. Rev., 145 (1966), 1156 | DOI | MR

[11] T. W. B. Kibble, Phys. Rev., 155 (1967), 1554 | DOI

[12] P. W. Anderson, Phys. Rev., 112 (1958), 1900 | DOI | MR

[13] R. Braut, Fazovye perekhody, «Mir», 1967

[14] A. N. Vasilev, A. K. Kazanskii, TMF, 14 (1973), 289 | MR

[15] A. N. Vasilev, A. K. Kazanskii, TMF, 15 (1973), 43 | MR