Contact transformations in Wheeler-Feynman electrodynamics
Annales de l'I.H.P. Physique théorique (1997)
- Volume: 66, Issue: 3, page 293-322
- ISSN: 0246-0211
Access Full Article
topHow to cite
topYaremko, Yurij. "Contact transformations in Wheeler-Feynman electrodynamics." Annales de l'I.H.P. Physique théorique 66.3 (1997): 293-322. <http://eudml.org/doc/76754>.
@article{Yaremko1997,
author = {Yaremko, Yurij},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {-body Lagrangian system; infinite jet bundle; constraints; single-time local perturbative expansions},
language = {eng},
number = {3},
pages = {293-322},
publisher = {Gauthier-Villars},
title = {Contact transformations in Wheeler-Feynman electrodynamics},
url = {http://eudml.org/doc/76754},
volume = {66},
year = {1997},
}
TY - JOUR
AU - Yaremko, Yurij
TI - Contact transformations in Wheeler-Feynman electrodynamics
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 66
IS - 3
SP - 293
EP - 322
LA - eng
KW - -body Lagrangian system; infinite jet bundle; constraints; single-time local perturbative expansions
UR - http://eudml.org/doc/76754
ER -
References
top- [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. Zbl0034.27801MR32447
- [2] E.H. Kerner, Hamiltonian formulation of action-at-a-distanse in electrodynamics, J. Math. Phys., Vol. 3, 1, 1962, pp. 35-42. Zbl0102.20704MR136278
- [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. MR1063631
- [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. MR914161
- [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. MR1019734
- [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. Zbl0775.70025MR1083096
- [9] R.P. Gaida, Non-Point Transformations in Classical Mechanics, Prepr. ICMP-94-5E, Lviv (Ukraine), 1994. Zbl1080.70515
- [10] D.J. Saunders, The Geometry of Jet Bundles, London Math. Soc., Lecture Notes Series 142, Cambridge Univ. Press, 1989. Zbl0665.58002MR989588
- [11] W.M. Tulczyjew, Sur la différentiellee de Lagrange, C. R. Acad. Sci. Paris, T. 280, Sér. A, 1975, pp. 1295-1298. Zbl0314.58018MR377987
- [12] O. Krupková, A geometrical setting for higher order Dirac-Bergmann theory of constraints, J. Math. Phys., Vol. 35, 12, 1994, pp. 6557-6576. Zbl0823.70016MR1303063
- [13] I. Bucur and A. Deleanu, Introduction to the Theory of Categories and Functors, John Wiley & Sons, London.New York.Sydney, 1968. Zbl0197.29205
- [14] N.H. Ibragimov and R.L. Anderson, Lie-Bäcklund tangent transformations, J. Math. Anal. Appl., Vol. 59, 1, 1977, pp. 145-162. Zbl0355.35004MR480853
- [15] N.H. Ibragimov, Group theoretical nature of conservation theorem, Letters in Math. Phys., Vol. 1, 5, 1977, pp. 423-428. Zbl0346.35074MR443001
- [16] D.M. Gitman and I.V. Tyutin, Canonical Quantization of Fields with Constraints, Nauka, Moscow, 1986 (in Russian). MR868276
- [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. Zbl0745.70013MR1067827
- [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. Zbl0581.58015MR808964
- [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. Zbl0778.58025MR1130547
- [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. Zbl0845.70012MR1341980
- [22] M. De León and P.R. Rodrigues, Methods of Differential Geometry in Analytical Mechanics, North-Holland Math. Studies, Ser. 158, Amsterdam, 1989. Zbl0687.53001MR1021489
- [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. Zbl0418.58010MR506712
- [24] A.D. Fokker, Ein invarianter Variationsatz für die Bewegung mehrerer elektrischer Massenteilchen, Z. Phys., Vol. 28, 5-6, 1929, pp. 386-393. Zbl55.0522.03JFM55.0522.03
- [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.
- [28] A. Staruszkiewicz, An example of a consistent relativistic mechanics of point particles, Ann. der Physik, Vol. 25, 4, 1970, pp. 362-367.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.