Noether transformations with vanishing conserved quantity
Gràcia, Xavier ; Pons, Josep M.
Annales de l'I.H.P. Physique théorique, Tome 61 (1994), p. 315-327 / Harvested from Numdam
Publié le : 1994-01-01
@article{AIHPA_1994__61_3_315_0,
     author = {Gr\`acia, Xavier and Pons, Josep M.},
     title = {Noether transformations with vanishing conserved quantity},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {61},
     year = {1994},
     pages = {315-327},
     mrnumber = {1311070},
     zbl = {0811.70013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1994__61_3_315_0}
}
Gràcia, Xavier; Pons, Josep M. Noether transformations with vanishing conserved quantity. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) pp. 315-327. http://gdmltest.u-ga.fr/item/AIHPA_1994__61_3_315_0/

[1] X. Gràcia and J.-M. Pons, A Hamiltonian Approach to Lagrangian Noether Transformations, J. Phys. A: Math. Gen., Vol. 25, 1992, pp. 6357-6369. | MR 1196870 | Zbl 0771.58015

[2] C. Batlle, J. Gomis, J.-M. Pons and N. Román-Roy, Equivalence between the Lagrangian and Hamiltonian Formalisms for Constrained Systems, J. Math. Phys., Vol. 27, 1986, pp. 2953-2962. | MR 866595 | Zbl 0613.70012

[3] J.-M. Pons, New Relations between Hamiltonian and Lagrangian Constraints, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 2705-2715. | MR 953447 | Zbl 0658.70016

[4] X. Gràcia and J.-M. Pons, On an Evolution Operator Connecting Lagrangian and Hamiltonian Formalisms, Lett. Math. Phys., Vol. 17, 1989, pp. 175-180. | MR 995795 | Zbl 0689.58016

[5] X. Gràcia, J.-M. Pons and N. Román-Roy, Higher-Order Lagrangian Systems: Geometric Structures, Dynamics, and Constraints, J. Math. Phys., Vol. 32, 1991, pp. 2744-2763. | MR 1130547 | Zbl 0778.58025

[6] X. Gràcia and J.-M. Pons, Gauge Transformations, Dirac's Conjecture and Degrees of Freedom for Constrained System, Ann. Phys., (N.Y.), Vol. 187, 1988, pp. 355-368. | MR 980754

[7] A.E. Noether, Invariante Variationsprobleme, Nachr. König. Gesell. Wissen. Göttingen, Math.-Phys. Kl., 1918, pp. 235-257. | JFM 46.0770.01

[8] E. Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik, Math. Ann., Vol. 84, 1921, pp. 258-276. | JFM 48.0877.02 | MR 1512036

[9] E.L. Hill, Hamilton's Principle and the Conservation Theorems of Mathematical Physics, Rev. Mod. Phys., Vol. 23, 1951, pp. 253-260. | MR 44959 | Zbl 0044.38509

[10] J. Rosen, Generalized Noether's theorem. I. Theory, Ann. Phys. (N.Y.), Vol. 82, 1974, pp. 54-69. | MR 332060

[11] P.J. Olver, Applications of Lie Groups to Differential Equations, GTM 107, Springer, New York, 1986. | MR 836734 | Zbl 0588.22001

[12] J.-F. Cariñena, C. López and E. Martínez, A New Approach to the Converse of Noether's theorem, J. Phys. A: Math. Gen., Vol. 22, 1989, pp. 4777-4786. | MR 1023501 | Zbl 0739.58016

[13] C. Ferrario and A. Passerini, Symmetries and Constants of Motion for Constrained Lagrangian Systems: a Presymplectic Version of the Noether Theorem, J. Phys. A: Math. Gen., Vol. 23, 1990, pp. 5061-5081. | MR 1083892 | Zbl 0708.70018

[14] L. Lusanna, The second Noether Theorem as the Basis of the Theory of Singular Lagrangians and Hamiltonian Constraints, Riv. Nuovo Cim., Vol. 14 (3), 1991 | MR 1111890

[15] M. Henneaux, Lectures on the antifield-BRST Formalism for Gauge Theories, Nucl. Phys. B (Proc. Suppl.), Vol. 18A, 1990, pp. 47-105. | MR 1128793 | Zbl 0957.81711

[16] I.A. Batalin and G.A. Vilkovisky, Closure of the Gauge Algebra, Generalized Lie Equations and Feynman Rules, Nucl. Phys. B, Vol. 234, 1984, pp. 106-124. | MR 736479

[17] J.-L. Anderson and P.G. Bergmann, Constraints in Covariant Field Theory, Phys. Rev., Vol. 83, 1951, pp. 1018-1025. | MR 44382 | Zbl 0045.45505

[18] L. Castellani, Symmetries in Constrained Hamiltonian Dynamics, Ann. Phys. (N.Y.), Vol. 143, 1982, pp. 357-371. | MR 682973

[19] J. Gomis, K. Kamimura and J.-M. Pons, To Construct Gauge Transformations from Singular Lagrangians, Europhys. Lett., Vol. 2, 1986, pp. 187-194.

[20] J. Gomis, M. Henneaux and J.-M. Pons, Existence Theorem for Gauge Symmetries in Hamiltonian Constrained Systems, Class. Quantum Grav., Vol. 7, 1990, pp. 1089-1096. | MR 1053325 | Zbl 0697.58022

[21] C. Batlle, J. Gomis, X. Gràcia and J.-M. Pons, Noether's Theorem and Gauge Transformations: Application to the Bosonic String and CPn-12 Model, J. Math. Phys., Vol. 30, 1989, pp. 1345-1350. | MR 995780 | Zbl 0689.53051