Contact transformations in Wheeler-Feynman electrodynamics
Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 3, p. 293-322
@article{AIHPA_1997__66_3_293_0,
     author = {Yaremko, Yurij},
     title = {Contact transformations in Wheeler-Feynman electrodynamics},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {66},
     number = {3},
     year = {1997},
     pages = {293-322},
     zbl = {0885.70016},
     mrnumber = {1456515},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1997__66_3_293_0}
}
Yaremko, Yurij. Contact transformations in Wheeler-Feynman electrodynamics. Annales de l'I.H.P. Physique théorique, Volume 66 (1997) no. 3, pp. 293-322. http://www.numdam.org/item/AIHPA_1997__66_3_293_0/

[1] J.A. Wheeler and R.P. Feynman, Classical electrodynamics in terms of direct interparticle action, Rev. Mod. Phys., Vol. 21, 3, 1949, pp. 425-433. | MR 32447 | Zbl 0034.27801

[2] E.H. Kerner, Hamiltonian formulation of action-at-a-distanse in electrodynamics, J. Math. Phys., Vol. 3, 1, 1962, pp. 35-42. | MR 136278 | Zbl 0102.20704

[3] C.G. Darwin, The dynamical motions of charged particles, Philos. Mag., Vol. 39, 233, 1920, pp. 537-551.

[4] J.Z. Simon, Higher-derivative Lagrangians, nonlocality, problems, and solutions, Phys. Rev. D, vol.41, 12, 1990, pp. 3720-3733. | MR 1063631

[5] R.P. Gaida, Yu.B. Kluchkovsky, and V.I. Tretyak, Three-Dimensional Lagrangian Approach to the Classical Relativistic Dynamics of Directly Interacting Particles, Constraint's Theory and Relativistic Dynamics, Arcetri, Firenze (Italy), May 28-30, 1986. Ed. by G. Longhi and L. Lusanna, World Scientific, Singapore, 1987, pp. 210-241. | MR 914161

[6] X. Jaén, J. Llosa, and A. Molina, A reduction of order two for infinite-order Lagrangians, Phys. Rev. D., Vol. 34, 8, 1986, pp. 2302-2311.

[7] D.A. Eliezer and R.P. Woodard, The problem of nonlocality in string theory, Nucl. Phys. B., Vol. 325, 1989, pp. 389-469. | MR 1019734

[8] T. Damour and G. Shäfer, Redefinition of position variables and the reduction of higher-order Lagrangians, J. Math. Phys., Vol. 32, 1, 1991, pp. 127-134. | MR 1083096 | Zbl 0775.70025

[9] R.P. Gaida, Non-Point Transformations in Classical Mechanics, Prepr. ICMP-94-5E, Lviv (Ukraine), 1994.

[10] D.J. Saunders, The Geometry of Jet Bundles, London Math. Soc., Lecture Notes Series 142, Cambridge Univ. Press, 1989. | MR 989588 | Zbl 0665.58002

[11] W.M. Tulczyjew, Sur la différentiellee de Lagrange, C. R. Acad. Sci. Paris, T. 280, Sér. A, 1975, pp. 1295-1298. | MR 377987 | Zbl 0314.58018

[12] O. Krupková, A geometrical setting for higher order Dirac-Bergmann theory of constraints, J. Math. Phys., Vol. 35, 12, 1994, pp. 6557-6576. | MR 1303063 | Zbl 0823.70016

[13] I. Bucur and A. Deleanu, Introduction to the Theory of Categories and Functors, John Wiley & Sons, London.New York.Sydney, 1968. | Zbl 0197.29205

[14] N.H. Ibragimov and R.L. Anderson, Lie-Bäcklund tangent transformations, J. Math. Anal. Appl., Vol. 59, 1, 1977, pp. 145-162. | MR 480853 | Zbl 0355.35004

[15] N.H. Ibragimov, Group theoretical nature of conservation theorem, Letters in Math. Phys., Vol. 1, 5, 1977, pp. 423-428. | MR 443001 | Zbl 0346.35074

[16] D.M. Gitman and I.V. Tyutin, Canonical Quantization of Fields with Constraints, Nauka, Moscow, 1986 (in Russian). | MR 868276 | Zbl 1072.81501

[17] P.W. Hebda, Treatment of higher-order Lagrangians via the construction of dynamically equivalent first-order Lagrangians, J. Math. Phys., Vol. 31, 9, 1990, pp. 2116-2125. | MR 1067827 | Zbl 0745.70013

[18] M. Ostrogradski, Mémoire sur les équations différentielles relatives aux problèmes des isopérimètres, Mem. Acad. St.-Pétersbourg, Vol. VI, 1850, pp. 385-517.

[19] M. De León and P.R. Rodrigues, Generalized Classical Mechanics and Field Theory, North-Holland Math. Studies, Ser. 112, Amsterdam, 1985. | MR 808964 | Zbl 0581.58015

[20] X. Gràcia, J.M. Pons and N. Román-Roy, Higher-order Lagrangian systems Geometric structures, dynamics, and constraints, J. Math. Phys., Vol. 32, 10, 1991, pp. 2744-2763. | MR 1130547 | Zbl 0778.58025

[21] M. De León and D.M. De Diego, Symmetries and constants of the motion for higher-order Lagrangian systems, J. Math. Phys., Vol. 36, 8, 1995, pp. 4138-4161. | MR 1341980 | Zbl 0845.70012

[22] M. De León and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North-Holland Math. Studies, Ser. 158, Amsterdam, 1989. | MR 1021489 | Zbl 0687.53001

[23] M.J. Gotay, J.M. Nester and G. Hinds, Presymplectic manifolds and the Dirac-Bergmann theory of constraints, J. Math. Phys., Vol. 19, 11, 1978, pp. 2388-2399. | MR 506712 | Zbl 0418.58010

[24] A.D. Fokker, Ein invarianter Variationsatz für die Bewegung mehrerer elektrischer Massenteilchen, Z. Phys., Vol. 28, 5-6, 1929, pp. 386-393. | JFM 55.0522.03

[25] R.P. Gaida and V.I. Tretyak, Single-time form of the Fokker-type relativistic dynamics.I, Acta Phys. Pol., Vol. B11, 7, 1980, pp. 509-522.

[26] R.P. Gaida, Yu. B. Kluchkovsky, and V.I. Tretyak, Lagrangian classical relativistic mechanics of a system of directly interacting particles.I, Theor. Math. Phys., Vol. 44, 2, 1980, pp. 687-697.

[27] A. Staruszkiewicz, Canonical theory of the two-body problem in the classical relativistic electrodynamics, Ann. Inst. H. Poincaré, Vol. 14, 1, 1971, pp. 69-77. | Numdam

[28] A. Staruszkiewicz, An example of a consistent relativistic mechanics of point particles, Ann. der Physik, Vol. 25, 4, 1970, pp. 362-367.