Invariant variational problems and conservation laws (remarks on Noether's theorem)
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 3, pp. 350-359
N. Kh. Ibragimov. Invariant variational problems and conservation laws (remarks on Noether's theorem). Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 3, pp. 350-359. http://geodesic.mathdoc.fr/item/TMF_1969_1_3_a4/
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Noether's theorem on the conservation !aws for invariant variational problems is generalized. All the conservation laws for the Dirae equations are found in an illustration of the generalization.

[1] E. Noether, Gottingen Nachrichten, Math.- Phys. Kl., 2 (1918), 235; Variatsionnye printsipy mekhaniki, Sb., Fizmatgiz, 1959, 611–630 | MR

[2] E. Bessel-Hagen, Math. Ann., 84 (1921), 258 | DOI | MR | Zbl

[3] E. L. Hill, Revs. Mod., 23 (1951), 253 | DOI | Zbl

[4] W. Pauli, Nuovo Cim., 6 (1957), 204 | DOI | MR | Zbl

[5] L. P. Eizenkhart, Nepreryvnye gruppy preobrazovanii, IL, 1947

[6] L. V. Ovsyannikov, Gruppovye svoistva differentsialnykh uravnenii, Izd-vo SO AN SSSR, 1962 | MR

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

[8] F. Engel, K. Faber, Die Liesche Theorie der partiellen Differentialgleichungen erster Ordnung, Leipzig, 1932 | MR

[9] N. Kh. Ibragimov, DAN SSSR, 178 (1968), 566 | MR

[10] N. Kh. Ibragimov, DAN SSSR, 185 (1969), 1226