@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, Volume 31 (1979) no. 2, pp. 115-139. http://archive.numdam.org/item/AIHPA_1979__31_2_115_0/
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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.
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,