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Prog. Theor. Phys. Vol. 54 No. 2 (1975) pp. 563-577

[ Full Text PDF : FREE ACCESS (1229K) ]

Relativistic Mechanics of Two Interacting Particles and Bilocal Theory

Takehiko Takabayasi

Department of Physics, Nagoya University, Nagoya

(Received February 10, 1975)

Abstract:

New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical fundation and internal dynamics.
As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories.


URL : http://ptp.ipap.jp/link?PTP/54/563/
DOI : 10.1143/PTP.54.563

[ Full Text PDF : FREE ACCESS (1229K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 331-332 :
    Relativistic Mechanics of Bilocal and Trilocal Structures
    Takehiko Takabayasi
  2. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 1081-1083 :
    Relativistic Mechanics of Two Interacting Particles with Mass
    Tohru Sohkawa
  3. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1806-1808 :
    Slopes of Meson Trajectories
    Takehiko Takabayasi
  4. Progress of Theoretical Physics Vol. 57 No. 6 (1977) pp. 2127-2143 :
    Relativistic Mechanics of Interacting Particles and Multi-Local Theory. I
    Takehiko Takabayasi and Seiji Kojima
  5. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 667-686 :
    Relativistic Mechanics for Two and Three Particles
    Masashi Fujigaki
  6. Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1299-1315 :
    Relativistic Mechanics of Interacting Particles and Multi-Local Theory. II
    Takehiko Takabayasi
  7. Progress of Theoretical Physics Vol. 58 No. 5 (1977) pp. 1635-1644 :
    The New Wave Equation of the Bi-Local Field and Its Mechanical Model
    Tetsuo Gotō
  8. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1947-1953 :
    Elimination of Relative Time in Bilocal Model
    Kiyoshi Kamimura
  9. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 633-645 :
    The Interaction of the Bi-Local Field with the External Field
    Tetsuo Gotō and Kiyoshi Kamimura
  10. Progress of Theoretical Physics Vol. 59 No. 4 (1978) pp. 1330-1345 :
    A New Relativistic Mechanics for Two-Particle System
    Masashi Fujigaki and Seiji Kojima
  11. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1746-1754 :
    Scattering Amplitude of Bi-Local Field in External Source
    Kiyoshi Kamimura and Tadayoshi Shimizu
  12. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2133-2148 :
    Constraints, Center-of-Masses and Quantization for Relativistically Structured Systems
    Takehiko Takabayasi and Kenji Takeuchi
  13. Progress of Theoretical Physics Vol. 60 No. 2 (1978) pp. 595-610 :
    Constituent Mass, Free-Limit Condition, and Quantization for Trilocal Theory
    Takehiko Takabayasi
  14. Progress of Theoretical Physics Vol. 61 No. 3 (1979) pp. 960-970 :
    Relativistic Two-Particle System and Spin-Mass Relations of Meson
    Seiji Kojima
  15. Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1235-1250 :
    Covariant Wave Equations of Two Spinning Particles Harmonically Bound
    Takehiko Takabayasi
  16. Progress of Theoretical Physics Vol. 62 No. 4 (1979) pp. 1143-1151 :
    Bi-Local Field on Space-Like Surface
    Kiyoshi Kamimura
  17. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1466-1476 :
    New Formalism for Simple Relativistic Oscillator Model and Electromagnetic Interaction
    Takehiko Takabayasi
  18. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1323-1330 :
    Relativistic Harmonic Oscillator Quark Model with Unequal Quark Masses
    Shin Ishida and Takashi Sonoda
  19. Progress of Theoretical Physics Supplement No.67 (1979) pp. 1-68 :
    Relativistic Mechanics of Confined Particles as Extended Model of Hadrons
    Takehiko Takabayasi
  20. Progress of Theoretical Physics Supplement No.86 (1986) pp. 81-92 :
    Theory of Relativistic String and Multilocal Model
    Takehiko Takabayasi

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