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Prog. Theor. Phys. Vol. 71 No. 5 (1984) pp. 1051-1062
Lagrangian Formulation of Todorov-Komar Model
J. Gomis,
Kiyoshi Kamimura* and
J. M. Pons
Departament de Física Teòrica, Universitat de Barcelona, Diagonal 647, Barcelona-28
*Department of Physics, Toho University, Funabashi 274
(Received December 9, 1983)
Abstract:
The multi-temporal Hamiltonian model of relativistic particle interaction (Todorov-Komar model) is studied from the viewpoint of the Lagrangian formalism. The action is constructed and the gauge structure is clarified.
The mathematical coordinates used to describe the Lagrangian are not gauge invariant and are disqualified as the physical coordinates of the interacting particles. The position of the particles is defined as the function of the canonical variables so that the world lines are invariant under the gauge transformations.
URL :
http://ptp.ipap.jp/link?PTP/71/1051/
DOI : 10.1143/PTP.71.1051
References:
- L. Bel, Ann. Inst. H. Poincaré, 18A (1973), 57.
L. Bel and J. Martin, Ann. Inst. H. Poincaré, 22A (1975), 173.
- See, for example,
T. Takabayasi and T. Goto et al. in Prog. Theor. Phys. Suppl. No. 67 (1979).
G. Longhi, F. Rohlich and I. T. Todorov in “Relativistic Action at a Distance”, Lecture Note in Phys. 162 (Springer, 1982), ed. J. Llosa.
- J. Llosa, A. Marques and A. Molina, Ann. Inst. H. Poincaré, 32A (1980), 303.
D. Dominici, J. Gomis, J. A. Lobo and J. M. Pons, Nuovo Cim. 61B (1981), 306.
L. Lusanna, Nuovo Cim. 65B (1981), 135.
J. M. Pons, Ann. of Phys. to be published.
- P. A. M. Dirac, Can. J. Math. 2 (1950), 129; Lecture on Quantum Mechanics (New York, N. Y., 1964).
- T. Takabayasi and S. Kojima, Prog. Theor. Phys. 57 (1977), 2127[PTP].
- K. Kamimura and T. Shimizu, Prog. Theor. Phys. 58 (1977), 383[PTP].
K. Kamimura, Prog. Theor. Phys. 58 (1977), 1947[PTP].
D. Dominici, J. Gomis and G. Longhi, Nuovo Cim. 48B (1978), 152; ibid. 48A (1978), 257; ibid. 56B (1980), 263.
- I. T. Todorov, “Dynamics of Relativistic Point Particles as a Problem with Constraints”, Comm. JINRE 2-10125, Dubna (1976).
See also, I. T. Todorov in Ref. 2).
A. Komar, Phys. Rev. D18 (1978), 1881[APS];
ibid. D18 (1978), 1887[APS];
ibid. D18 (1978), 3617[APS];
ibid. D19 (1979), 2408[APS].
- Ph. Droz-Vincent, Reports on Math. Phys. 8 (1975), Ann. Inst. H. Poincaré, 27A (1977), 407.
- V. V. Molotkov and I. T. Todorov, Comm. Math. Phys. 79 (1981), 111.
G. Longhi, see Ref. 2).
E. C. G. Sudarshan, N. Mukunda and J. N. Goldberg, Phys. Rev. D23 (1981), 2218[APS].
- K. Kamimura, Nuovo Cim. 68B (1982), 33.
- E. Nöther, Nachr. Ges. Wiss. Gettingen, 2 (1981), 235.
G. Bergmann et al. Phys. Rev. 83 (1951), 1018[APS];
ibid. 89 (1953), 4[APS];
ibid. 98 (1953), 531[APS];
ibid. 103 (1956), 807[APS].
- For recent reviews see, for example,
M. J. Gotay, “Presymplectic Manifolds, Geometric Constraint Theory and Dirac-Bergmann Theory of Constraints” Maryland Ph. D thesis (1979);
G. R. Allcock, Kinam 2 (1980), 335.
- M. Lutzky, J. of Phys. A15 (1982), L87.
- R. Giachetti and E. Sorace, Lett. Nuovo Cim. 26 (1979), 1.