@article{AIHPA_1981__34_2_231_0, author = {Bel, L. and Martin, J.}, title = {Predictive relativistic mechanics of systems of {N} particles with spin. {II.} {The} electromagnetic interaction}, journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique}, pages = {231--252}, publisher = {Gauthier-Villars}, volume = {34}, number = {2}, year = {1981}, mrnumber = {610866}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1981__34_2_231_0/} }
TY - JOUR AU - Bel, L. AU - Martin, J. TI - Predictive relativistic mechanics of systems of N particles with spin. II. The electromagnetic interaction JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1981 SP - 231 EP - 252 VL - 34 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1981__34_2_231_0/ LA - en ID - AIHPA_1981__34_2_231_0 ER -
%0 Journal Article %A Bel, L. %A Martin, J. %T Predictive relativistic mechanics of systems of N particles with spin. II. The electromagnetic interaction %J Annales de l'institut Henri Poincaré. Section A, Physique Théorique %D 1981 %P 231-252 %V 34 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPA_1981__34_2_231_0/ %G en %F AIHPA_1981__34_2_231_0
Bel, L.; Martin, J. Predictive relativistic mechanics of systems of N particles with spin. II. The electromagnetic interaction. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 34 (1981) no. 2, pp. 231-252. http://archive.numdam.org/item/AIHPA_1981__34_2_231_0/
[1] Ann. Institut H. Poincaré, t. 23, 1980, p. 409.
and ,[2] Phys. Rev. Lett., t. 2, 1959, p. 435.
, and ,[3] See for example: Phys. Rev., t. D 7, 1973, p. 1099; and , Phys. Rev., t. D 8, 1973, p. 4347; , in Journées Relativistes de Toulouse, Université de Toulouse, Département de Mathé- matiques, 1974 ; et , Ann. Inst. H. Poincaré, t. 25, 1976, p. 411.
, and ,[4] Phys. Rev., t. 34, 1929, p. 553; Phys. Rev., t. 36, 1930, p. 383. A deduction of this Hamiltonian by Quantum Electrodynamic procedures may be found, in : LANDAU et LIFCHITZ, Théorie Quantique Relativiste (première partie), éditions Mir, Moscou, 1972. | JFM
,[5] A different classical derivation of the equations of motion and lagrangians relative to this Hamiltonian may be found, in : , Tesis doctoral, Universitat de Barcelona, 1978; and , preprint, Universitat Autonoma de Barcelona, Spain, 1979.
[6] It is assumed that the curve is time-like and future oriented. We take signature + 2 for M4. Einstein's summation convention will be utilized for all kinds of indices; these will always be placed in the appropriate position (« covariant » or « contravariant ») to respect the said convention.
[7] This condition eliminates the presence of an electric dipolar moment.
[8] We use the convention η0123 = + 1, and consequently η0123 = - 1.
[9] We here consider the advanced propagator as an open possibility.
[10] See for example: J. Math. Phys., t. 17, 1976, p. 1496.
and ,[11] Actually BARGMANN, MICHEL and TELEGDI only use these equations for the case of a homogeneous electromagnetic field. It should also be pointed out that similar Eqs. appear in the following: Phil. Mag., t. 3, 1927, p. 1; , Z. Physik, t. 37, 1926, p. 243; , Quantum Mechanics, North Holland Publishing Co., Amsterdam, 1957. In Kramer's equations there appear, nevertheless, certain inconsistencies, as is pointed out in Bargmann, Michel and Teledgi.
,[12] See for example: L. BEL and X. FUSTERO (ref. 3).
[13] See for example: Géométrie Différentielle et Systèmes Extérieurs, éd. Dunod, Paris, 1968. | MR | Zbl
,[14] In particular formulae (4.14 b) and (4.34) of BM.
[15] For the case of spinless particles consult ref. 12.
[16] For more details on Exterior Calculus techniques consult ref. 13.
[17] This part is already obtained from Darwin's well-known Lagrangian: , Phil. Mag., t. 39, 1920, p. 537.
[18] This term, which contains a Dirac « delta », is purely quantum mechanical. Consult the refs. at 4.
[19] Contribution to Differential Geometry and Relativity, Cahen and Flato (eds.), D. Reidel Publishing Co., Dordrecht, Holland, 1976. | MR
,