@article{AIHPA_1979__31_2_115_0, author = {Sanz, J. L.}, title = {Two charges in an external electromagnetic field : a generalized covariant hamiltonian formulation}, journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique}, pages = {115--139}, publisher = {Gauthier-Villars}, volume = {31}, number = {2}, year = {1979}, mrnumber = {561918}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1979__31_2_115_0/} }
TY - JOUR AU - Sanz, J. L. TI - Two charges in an external electromagnetic field : a generalized covariant hamiltonian formulation JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1979 SP - 115 EP - 139 VL - 31 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1979__31_2_115_0/ LA - en ID - AIHPA_1979__31_2_115_0 ER -
%0 Journal Article %A Sanz, J. L. %T Two charges in an external electromagnetic field : a generalized covariant hamiltonian formulation %J Annales de l'institut Henri Poincaré. Section A, Physique Théorique %D 1979 %P 115-139 %V 31 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1979__31_2_115_0/ %G en %F AIHPA_1979__31_2_115_0
Sanz, J. L. Two charges in an external electromagnetic field : a generalized covariant hamiltonian formulation. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 31 (1979) no. 2, pp. 115-139. http://archive.numdam.org/item/AIHPA_1979__31_2_115_0/
[1] 24 A, 1976, p. 347. | Numdam
and , Ann. Inst. H. Poincaré,[2] The proof of this theorem made by (Il Nuovo Cimento, 12 B, 1972, p. 1) is incorrect, but the theorem can be proven to be correct (see Section II).
[4] Phys. Rev., t. 142, 1966, p. 817. | MR
,[5] J. Math. Phys., t. 8, 1967, p. 201.
,[6] 12, 1970, p. 307. | Numdam | MR
, Ann. Inst. H. Poincaré, t.[7] Phys. Rev., 7 D, 1973, p. 1099.
, and ,[8] Il Nuovo Cimento, 20 B, 1974, p. 209.
and ,[9] Phys. Rev., 8 D, 1973, p. 4347.
and ,[10] Phys. Rev., 13 D, 1976, p. 2805.
and ,[11] Phys. Rev., 9 D, 1974, p. 2760.
and ,[12] Ann. Inst. H. Poincaré, 25, 1976, p. 411. | Numdam | Zbl
and ,[13] Lett. Il Nuovo Cimento, t. 1, 1969, p. 839.
,[14] Phys. Rev., 1 D, 1969, p. 2212.
,[15] Ann. Inst. H. Poincaré, t. 14, 1971, p. 189. | Numdam | MR
,[16] Doctoral course, Departamento de Fisica Teórica, Universidad de Barcelona, 1976.
,[19] Foundations of Mechanics, W. A. Benjamin, 1967. | Zbl
,[20] Géométrie diferentielle et Mécanique Analitique, Hermann, 1969. | MR | Zbl
,[21] Doctoral Course, Universidad Autónoma de Madrid, 1972, unpublished.
,[22] J. Math. Phys., Section 2.
and , to appear in[23] Let us consider a symplectic form on (TM4)N with local expression Ω = 1/2ΩABdyA dyB (A, B = 0, ... 8N - 1; yα = xα1, ..., y4(N - 1) + α = xαN, y4N+α = πα1, ..., y4(2N-1)+α = παN) where ΩAB are skewsymmetric functions on (TM4)N. The Poisson bracket of two functions f and g on (TM4)N is defined by [f, g] = - Ω-1AB∂f ∂yA∂g∂yB where Ω-1AB is the inverse matrix of ΩAB (i. e., Ω-1ABΩBC = δAC). As is well-known in the literature (see, for example, 18 A, 1973, p. 57 ; , Symposia Mathematica, t. 14, 1974, p. 53 ; J. Math. Phys., t. 15, 1974, p. 1033) condition (22) can be equivalently written in the form [xαa, xβb] = 0 ([, ] being the Poisson bracket relative to Ω), which is the classical form of expressing the canonical character of the position variables xαa.
, Ann. Inst. H. Poincaré, t.[24] J. Math. Phys.
, to be published in[25] Rev. Mod. Phys., t. 35, 1963, p. 350. | MR
, and ,[26] J. Math. Phys., t. 8, 1967, p. 1756.
,[27] J. Math. Phys., t. 19, 1978, p. 780.
and ,[28] J. Math. Phys., t. 15, 1974, p. 1689.
,[29] J. Math. Phys., t. 16, 1975, p. 1844.
,[30] 22 A, 1957, p. 173. | Numdam | MR
and , Ann. Inst. H. Poincaré,[32] Géométrie différentielle et systèmes extérieures, Dunod, 1968. | MR | Zbl
,[33] Tesis Doctoral, Universidad Autónoma de Madrid, 1976.
,