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Symmetries in relativistic dynamics of a charged particle. (English) Zbl 0339.53039

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
55R25 Sphere bundles and vector bundles in algebraic topology
70F99 Dynamics of a system of particles, including celestial mechanics

References:

[1] S. Abe and M. Ikeda , On groups of motions in space-time with a non-symmetric fundamental tensor g\mu \nu . I, II, Tensor, N. S. , vol. 10 , 1960 , p. 26 - 33 . Ibid., vol. 17 , 1966 , p. 288 - 299 . MR 201175 | Zbl 0108.41202 · Zbl 0108.41202
[2] S. Abe , On space-times with a non-symmetric fundamental tensor, admitting a sixparameter group of motions , Tensor, N. S. , vol. 18 , 1967 , p. 289 - 300 . An addendum to On space-times with... group of motions , Tensor N. S. , vol. 20 , 1969 , p. 210 - 212 . Zbl 0161.46401 · Zbl 0161.46401
[3] S. Abe , The generalized Killing vectors of the group of motions in X4(I ; G6) and X4(II ; G6). I, II , Tensor, N. S. , vol. 20 , 1969 , p. 289 - 298 . Ibid., vol. 21 , 1970 , p. 101 - 116 . Zbl 0181.49903 · Zbl 0181.49903
[4] S. Abe , The space-time with an anti-Mach metric and V4 (II), Tensor, N. S. , vol. 22 , 1971 , p. 261 - 268 . MR 299164 | Zbl 0223.53021 · Zbl 0223.53021
[5] L.C. Chen and T. Janssen , A charged particle in a uniform electromagnetic field . A group-theoretical analysis, Physica , vol. 77 , 1974 , p. 290 - 310 . MR 381515
[6] T. Iwai , On kinematical invariances of the equations of motion , Internat. J. Theoret. Phys. , vol. 12 , 1975 , p. 383 - 392 . MR 468428 | Zbl 0324.70019 · Zbl 0324.70019 · doi:10.1007/BF01808165
[7] S. Sasaki , On the differential geometry of tangent bundles of Riemannian manifolds . I, II, Tôhoku Math. J. , vol. 10 , 1958 , p. 338 - 354 . Ibid., vol. 14 , 1962 , p. 146 - 155 . Article | MR 112152 | Zbl 0086.15003 · Zbl 0086.15003 · doi:10.2748/tmj/1178244668
[8] J. Śniatycki and W.M. Tulczyjew , Canonical dynamics of relativistic charged particles , Ann. Inst. H. Poincaré , vol. 15 , 1971 , p. 177 - 187 . Numdam | MR 297309 | Zbl 0231.70013 · Zbl 0231.70013
[9] H. Takeno , Gravitational null field admitting a parallel null vector field. - The spacetimes H and P - , Tensor, N. S. , vol. 12 , 1962 , p. 197 - 218 . MR 148449 | Zbl 0111.42301 · Zbl 0111.42301
[10] S. Takizawa , On contact structures of real and complex manifolds , Tôhoku Math. J. , vol. 15 , 1963 , p. 227 - 252 . Article | MR 157331 | Zbl 0122.40704 · Zbl 0122.40704 · doi:10.2748/tmj/1178243807
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