Prog. Theor. Phys. Vol. 57 No. 6 (1977) pp. 2127-2143

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Relativistic Mechanics of Interacting Particles and Multi-Local Theory. I

— The Bilocal Case —

Takehiko Takabayasi and Seiji Kojima

Department of Physics, Nagoya University, Nagoya 464

(Received December 10, 1976)

Abstract:

Relativistic mechanics of two-particle system, where the two constituent particles are bound by an arbitrary scalar potential, is derived from a Lagrangian completely. This Lagrangian has a new kind of invariance which gives rise to a primary constraint responsible to the suppression of the relative time degree. The other primary constraint following from the Lagrangian determines the rest mass of the system as due to internal motion. These constraints, together with the Euler equations, define the relativistic mechanics of the system in such a way that it has clear physical interpretation. Equivalence of this theory with the relativistic mechanics of two interacting particles established in a previous paper is explicitly shown. Quantization and introduction of interactions are briefly explained.

URL : http://ptp.ipap.jp/link?PTP/57/2127/
DOI : 10.1143/PTP.57.2127

References:

T. Takabayasi, Prog. Theor. Phys. 54 (1975), 563, [PTP](referred to as I).
See also, Prog. Theor. Phys. 52 (1974), 1376[PTP].
An abstract of this paper is given in T. Takabayasi, Prog. Theor. Phys. 57 (1977), 331[PTP].
H. Yukawa, Phys. Rev. 77 (1950), 219[APS].
cf. T. Takabayasi, Prog. Theor. Phys. 57 (1977), 329[PTP].
P. A. M. Dirac, Can. J. Math. 2 (1950), 129; Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).
T. Takabayasi, Proceedings of Eighth Nobel Symposium, edited by N. Svartholm (Stockholm, 1968) p. 157 (See, p. 183-184 thereof); Prog. Theor. Phys. 38 (1967), 966[PTP]; ibid. 42 (1969), 1210[PTP]; ibid. 48 (1972), 1718[PTP].
S. Ishida and J. Otokozawa, Prog. Theor. Phys. 47 (1972), 2117[PTP].
Interaction among bilocal objects has been treated by T. Goto and S. Naka, Prog. Theor. Phys. 51 (1974), 299[PTP].

Citing Article(s) :

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Relativistic Mechanics of Interacting Particles and Multi-Local Theory. II

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Elimination of Relative Time in Bilocal Model

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