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Prog. Theor. Phys. Supplement No.67 (1979) pp. 69-114

On the Bi-Local Model and String Model

Tetsuo Gotō, Shigefumi Naka and Kiyoshi Kamimura^*

Atomic Energy Research Institute, College of Science and Technology, Nihon University, Tokyo 101
^*Theoretical Physics Institute and Department of Physics, The University of Alberta, Edmonton, Alberta

Abstract:

The mechanical models of the bi-local fields and the string models are discussed in the formal point of view. Since the formulation of the extended particle pictures has no unique way, there are various formulations even in the simplest bilocal models. We confine ourselves mainly in the formulations by following which the interactions have been investigated. The scattering amplitudes and the form factors are discussed qualitatively. Some comments on the subsidiary conditions suppressing the relative time freedom are given by following Dirac's formalism. A short discussion of the bi-local model with spin is also shown by introducing Grassmann variables as classical variables corresponding to spin freedom.
As to the string model, we have discussed various interesting but unsolved problems; namely, the electromagnetic interactions, the string with massive ends, the spinning string and so on. We have proposed tentative prescriptions for treating some of these problems. We also discuss the different point of view concerning the string model. That is, we show that the difference equation furnishes us the same result as that given by the string model.

URL : http://ptp.ipap.jp/link?PTPS/67/69/
DOI : 10.1143/PTPS.67.69

[ Full Text PDF : FREE ACCESS (2663K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. S. Sakata, Prog. Theor. Phys. 16 (1956), 686[PTP].
2. H. Yukawa, Prog. Theor. Phys. 3 (1948), 205[PTP]; Phys. Rev. 77 (1950), 219[APS].
3. O. Hara and T. Goto, Prog. Theor. Phys. Suppl. No. 41 (1968), 56[PTP].
4. The bi-local model with unequal masses is complicated because of the complex constraints.
   See the following papers:
   M. Fujigaki and S. Kojima, Prog. Theor. Phys. 59 (1978), 1330[PTP].
   S. Kojima, Prog. Theor. Phys. 61 (1979), 960[PTP].
5. T. Takabayasi, Nuovo Cim. 33 (1964), 668.
6. T. Gotō, Prog. Theor. Phys. 58 (1977), 1635[PTP].
7. T. Gotō, Prog. Theor. Phys. 58 (1977), 1973[PTP].
8. T. Takabayasi, Prog. Theor. Phys. 23 (1960), 915[PTP].
9. K. Kamimura, Prog. Theor. Phys. 58 (1977), 1947[PTP].
10. P. A. M. Dirac, Lecture on Quantum Mechanics (New York, N. Y., 1964).
11. R. Casalbuoni, Nuovo Cim. A 33 (1976), 115; ibid. 33 (1976), 389; Phys. Lett. B 62 (1976), 49.
12. K. Fujimura, T. Kobayashi and M. Namiki, Prog. Theor. Phys. 43 (1970), 73[PTP].
    S. Ishida, K. Konno and Y. Yamazaki, Prog. Theor. Phys. 47 (1972), 317[PTP].
    S. Ishida and J. Otokozawa, Prog. Theor. Phys. 47 (1972), 2117[PTP].
13. T. Gotō and S. Naka, Prog. Theor. Phys. 51 (1974), 299[PTP].
14. T. Gotō and K. Kamimura, Prog. Theor. Phys. 59 (1978), 633[PTP].
15. K. Kamimura and T. Shimizu, Prog. Theor. Phys. 59 (1978), 1746[PTP].
16. I. Sogami, Prog. Theor. Phys. 41 (1969), 1352[PTP].
    I. Sogami, Nuovo Cim. A 46 (1978), 78.
    I. Sogami, Lett. Nuovo Cim. 24 (1979), 411.
    I. Sogami and S. Nishino, Nuovo Cim. (in press).
17. A. Z. Capri and C. C. Chiang, Prog. Theor. Phys. 59 (1978), 996[PTP]; ibid. 59 (1978), 1376[PTP].
18. T. Gotō and J. Otokozawa, Prog. Theor. Phys. 45 (1971), 263[PTP].
    T. Gotō, J. Otokozawa and T. Obara, Prog. Theor. Phys. 45 (1971), 1967[PTP].
19. S. Tanaka, Prog. Theor. Phys. Suppl. No. 41 (1968), 194[PTP].
    M. Bando, T. Inoue, Y. Takada and S. Tanaka, Prog. Theor. Phys. 38 (1967), 715[PTP].
    S. Hamamoto and S. Tanaka, Prog. Theor. Phys. 38 (1967), 1411[PTP].
20. T. Goto and S. Naka, Proceedings of the International Symposium on High Energy Physics, Tokyo, 1973, p. 275.
21. Y. Nambu, Phys. Rev. D 4 (1971), 1193[APS].
    G. Konisi, S. Matsuda, Y. Nakawaki and T. Saito, Prog. Theor. Phys. 51 (1974), 1172[PTP].
22. T. Gotō and K. Kamimura, Contributed to the XIX International Conference on High Energy Physics, August 1978 (Tokyo).
    K. Kamimura, Prog. Theor. Phys. 62 (1979), 1143[PTP].
    B. M. Barbashov and V. V. Nesterenko, Theor. Math. Phys. 31 (1977), 291.
    See also the followings:
    K. Kikkawa and M. Sato, Phys. Rev. Letter 38 (1977), 1309[APS].
    M. Ida, Prog. Theor. Phys. 59 (1978), 1661[PTP].
    W. A. Bardeen, J. Bars, A. J. Hanson and R. D. Pecc, Phys. Rev. D 13 (1976), 2364[APS].
23. A. Chodos and C. B. Thorn, Nucl. Phys. B 72 (1974), 509[CrossRef].
24. P. Ramond, Phys. Rev. D 3 (1971), 2415[APS].
    A. Neveu and J. H. Schwarz, Nucl. Phys. B 31 (1971), 86[CrossRef]; Phys. Lett. B 35 (1971), 529[CrossRef].
25. S. Naka, Prog. Theor. Phys. 59 (1978), 2107[PTP].
    S. Naka, Prog. Theor. Phys. 62 (1979), 278[PTP].
26. S. Naka, Prog. Theor. Phys. 48 (1972), 1024[PTP].
27. H. Yukawa and Y. Katayama, Prog. Theor. Phys. Suppl. No. 41 (1968), 1[PTP].
    Y. Katayama, I. Umemura and H. Yukawa, Prog. Theor. Phys. Suppl. No. 41 (1968), 22[PTP].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 1065-1078 :

   Superfield Approach to Systems of Two and Three Spinning Particles

   Shigefumi Naka, Seiji Kojima and Hiroshi Kaseno

2. 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

3. Progress of Theoretical Physics Vol. 71 No. 3 (1984) pp. 648-655 :

   Elimination of Redundant Variables in a Partially Supersymmetric Bi-Local Model

   Shigefumi Naka and Hiroshi Kakuhata

4. Progress of Theoretical Physics Vol. 109 No. 1 (2003) pp. 103-114 :

   5-Dimensional Spacetime with q-Deformed Extra Dimension

   Shigefumi Naka and Haruki Toyoda

5. Progress of Theoretical Physics Vol. 113 No. 3 (2005) pp. 645-656 :

   q-Deformed Bi-Local Fields

   Shigefumi Naka, Haruki Toyoda and Aiko Kimishima

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