Relativistic hamiltonian dynamics of singularities of the Liouville equation

A. K. Pogrebkov; I. T. Todorov

Annales de l'I.H.P. Physique théorique (1983)

  • Volume: 38, Issue: 1, page 81-92
  • ISSN: 0246-0211

How to cite


Pogrebkov, A. K., and Todorov, I. T.. "Relativistic hamiltonian dynamics of singularities of the Liouville equation." Annales de l'I.H.P. Physique théorique 38.1 (1983): 81-92. <>.

author = {Pogrebkov, A. K., Todorov, I. T.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Hamiltonian description; dynamics of singularities; Liouville equation; Markov-Yukawa gauge},
language = {eng},
number = {1},
pages = {81-92},
publisher = {Gauthier-Villars},
title = {Relativistic hamiltonian dynamics of singularities of the Liouville equation},
url = {},
volume = {38},
year = {1983},

AU - Pogrebkov, A. K.
AU - Todorov, I. T.
TI - Relativistic hamiltonian dynamics of singularities of the Liouville equation
JO - Annales de l'I.H.P. Physique théorique
PY - 1983
PB - Gauthier-Villars
VL - 38
IS - 1
SP - 81
EP - 92
LA - eng
KW - Hamiltonian description; dynamics of singularities; Liouville equation; Markov-Yukawa gauge
UR -
ER -


  1. [1] G.P. Jorjadze, A.K. Pogrebkov, M.C. Polivanov, , ICTP preprint IC/78/126. Trieste, 1978. 2 
  2. G.P. Georjadze, A.K. Pogrebkov, M.K. Polivanov, , Theor. Math. Phys., t. 40, 1979, p. 706-715. Zbl0453.35058
  3. [2] A.K. Pogrebkov, Complete integrability of dynamical systems, generated by the singular solutions of the Liouville equation, Theor. Math. Phys., t. 45, 1980. p. 951-957. Zbl0461.35083MR604518
  4. [3] D.G. Currie, T.F. Jordan, E.C.G. Sudarshan, Relativistic invariance and Hamiltonian theories of interacting particles, Rev. Mod. Phys., t. 35, 1963, p. 350-375; ibid1032. MR151138
  5. [4] H. Leutwyler, A no-interaction theorem in classical relativistic Hamiltonian particle mechanics, Nuovo Cim., 37, 1965, p. 556-557. 
  6. [5] R.N. Hill, Canonical formulation of relativistic mechanics, J. Math. Phys., t. 8, 1967, p. 1756-1773. 
  7. [6] R. Giachetti, E. Sorace, Nonexistence of two body interacting Lagrangians invariant under independent reparametrizations of each world-line, Lett. Nuovo Cim., t. 26, 1979, p. 1-4. 
  8. [7] V.V. Molotkov, I.T. Todorov, Frame dependence of world lines for directly interacting classical relativistic particles, Int. Rep. IC/79/59 Trieste, 1979. 
  9. [8] V.V. Molotkov, T.T. Todorov, Gauge dependence of world lines and invariance of the S-matrix in relativistic classical mechanics, Comm. Math. Phys., t. 79, 1981, p. 111-132. MR609231
  10. [9] I.T. Todorov, Dynamics of relativistic point particles as a problem with constraints, Commun. JINR E2-10125 Dubna, 1976; Constraint Hamiltonian mechanics of directly interacting relativistic paricles, preprint BI-TP 81/24, Bielefeld, 1981 ; Differential geometric methods in relativistic particle dynamics. Single particle systems, Lecture notes, USP Mathematizierung, Bielefeld, 1981 (This latter reference contains an extended bibliography). 
  11. [10] L.D. Faddeev, Feynman integrals for singular Lagrangians, Theor. Math. Phys., t. 1, 1969, p. 1-13. Zbl1183.81090
  12. [11] E.H. Kerner, Can the position variable be a canonical coordinate in a many particle relativistic theory?J. Math. Phys., t. 6, 1965, p. 1218-1227. MR187870
  13. [12] Ph. Droz-Vincent, Relativistic systems of interacting particles, Physica Scripta, t. 2, 1970, p. 129-134; N-body relativistic systems, Ann. Inst. H. Poincaré, t. 32A, 1980, p. 377-389. Zbl1063.83553MR309506
  14. [13] L. Bel, J. Martin, Formes Hamiltoniennes et systèmes conservatifs, Ann. Inst. H. Poincaré, t. 22A, 1975, p. 173-195. MR378697
  15. [14] H. Sazdjian, Position variables in classical relativistic Hamiltonian mechanics, Nucl. Phys., t. B161, 1979, p. 469-492. MR551949
  16. [15] P.A. Nikolov, I.T. Todorov, Space-time versus phase space approach to relativistic particle dynamics, Lecture Notes in Mathematics (to be published). Zbl0525.70018

NotesEmbed ?


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.