Contact transformations in Wheeler-Feynman electrodynamics

Yurij Yaremko

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 66, Issue: 3, page 293-322
  • ISSN: 0246-0211

How to cite

top

Yaremko, 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. [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. [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. [3] C.G. Darwin, The dynamical motions of charged particles, Philos. Mag., Vol. 39, 233, 1920, pp. 537-551. 
  4. [4] J.Z. Simon, Higher-derivative Lagrangians, nonlocality, problems, and solutions, Phys. Rev. D, vol.41, 12, 1990, pp. 3720-3733. MR1063631
  5. [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. [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. [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. [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. [9] R.P. Gaida, Non-Point Transformations in Classical Mechanics, Prepr. ICMP-94-5E, Lviv (Ukraine), 1994. Zbl1080.70515
  10. [10] D.J. Saunders, The Geometry of Jet Bundles, London Math. Soc., Lecture Notes Series 142, Cambridge Univ. Press, 1989. Zbl0665.58002MR989588
  11. [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. [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. [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. [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. [15] N.H. Ibragimov, Group theoretical nature of conservation theorem, Letters in Math. Phys., Vol. 1, 5, 1977, pp. 423-428. Zbl0346.35074MR443001
  16. [16] D.M. Gitman and I.V. Tyutin, Canonical Quantization of Fields with Constraints, Nauka, Moscow, 1986 (in Russian). MR868276
  17. [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. [18] M. Ostrogradski, Mémoire sur les équations différentielles relatives aux problèmes des isopérimètres, Mem. Acad. St.-Pétersbourg, Vol. VI, 1850, pp. 385-517. 
  19. [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. [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. [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. [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. [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. [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. [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. [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. [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. [28] A. Staruszkiewicz, An example of a consistent relativistic mechanics of point particles, Ann. der Physik, Vol. 25, 4, 1970, pp. 362-367. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.