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Prog. Theor. Phys. Vol. 48 No. 5 (1972) pp. 1718-1741

[ Full Text PDF : FREE ACCESS (1739K) ]

Bilocal Wave Equation for Baryons Lying on Linear Trajectories and Its Extension to a Linear Chain Model

Takehiko Takabayasi

Department of Physics, Nagoya University, Nagoya

(Received March 14, 1972)

Abstract:

A new bilocal wave equation for baryonic states is presented. It is a first-order differential equation containing three independent Dirac matrices, one of which is associated to the internal extension. The presence of three Dirac matrices assimilates three quark spins. The wave equation represents baryonic states lying on parallel linear trajectories. From the requirement for the existence of conserved current the model predicts that the intercept of the leading trajectory should be less than 1/2, in accord with observation. The corresponding bilocal theory for mesons requiring the introduction of two independent Dirac matrices is stated briefly. The generalization to the linear multilocal case which represents a one-dimensional chain consisting on N discrete points is performed and is analysed by the aid of normal mode expansion. The strong and electromagnetic interactions can be introduced to the model, though the theory is still at the non-second-quantized level. In the limit N → ∞ the chain model goes over to the “double Dirac string model” which is relevant to derivation of the dual amplitude, and this limiting transition from the discrete to the continuous case clarifies the boundary conditions and other subtleties for the latter model.


URL : http://ptp.ipap.jp/link?PTP/48/1718/
DOI : 10.1143/PTP.48.1718

[ Full Text PDF : FREE ACCESS (1739K) ] Citation:

References:

  1. H. Yukawa, Phys. Rev. 91 (1953), 415[APS]; ibid. 91 (1953), 416[APS].
  2. T. Takabayasi, Prog. Theor. Phys. 34 (1965), 124[PTP]; ibid. 38 (1967), 966[PTP]; Prog. Theor. Phys. Suppl. No. 41 (196), 130[PTP].
  3. D. Ito, Soryusiron Kenkyu (mimeographed circular in Japanese) 41 (1971), 5.
    K. Fujimura, T. Kobayashi and M. Namiki, Prog. Theor. Phys. 43 (1970), 73[PTP]; ibid. 44 (1970), 193[PTP].
    S. Ishida and J. Otokozawa, Prog. Theor. Phys. 47 (1972), 2117[PTP].
    Y. Nambu, Proceedings of Nobel Symposium on Elementary Particle Theory (1968), p. 105.
    Otherwise there have been papers which employ a higher-order wave equation to embody linear trajectories into bilocal model.
    Cf. T. Shirafuji, Prog. Theor. Phys. 39 (1968), 1047[PTP];
    T. Takabayasi, Prog. Theor. Phys. 42 (1969), 423[PTP]; ibid. 42 (1969), 1210[PTP].
  4. T. Takabayasi, Prog. Theor. Phys. 44 (1970), 1429[PTP]; ibid. 46 (1971), 1528[PTP]; ibid. 46 (1971), 1924[PTP].
  5. T. Takabayasi, Prog. Theor. Phys. 47 (1972), 1026[PTP].
  6. T. Takabayasi, Nuovo Cim. 23 (1962), 222.
  7. Various nonlocal spinor wave equations have been considered in the literature since H. Yukawa, Phys. Rev. 77 (1950), 219[APS].
    Examples of more recent papers are
    T. Takabayasi, Phys. Rev. 139 (1965), 1381[APS];
    H. S. Green, Proceedings of International Conf. on Elementary Particles, Kyoto (1965), p. 159;
    D. Ito, Soryusiron Kenkyu (mimeographed circular in Japanese) 43 (1971), 12;
    P. A. Cook, Lett. Nuovo Cim. 1 (1971), 419.
  8. T. Takabayasi, Prog. Theor. Phys. 43 (1970), 1117[PTP].
  9. Y. Nambu, Proceedings of International Conference on Symmetries and Quark Models (1969), p. 269.
    L. Susskind, Nuovo Cim. A 69 (1970), 457.
  10. P. Ramond, Phys. Rev. D 3 (1971), 2415[APS].
    Y. Aharonov, A. Casher and L. Susskind, Phys. Lett. B 35 (1971), 512[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 51 No. 1 (1974) pp. 262-283 :
    Theory of Relativistic String and Super-Wave Equation. I
    Takehiko Takabayasi
  2. Progress of Theoretical Physics Vol. 52 No. 4 (1974) pp. 1376-1391 :
    Relativistic Bound State under the Hooke-Type Action-at-a-Distance
    Takehiko Takabayasi
  3. Progress of Theoretical Physics Vol. 53 No. 3 (1975) pp. 803-809 :
    Electromagnetic Property of the Double Dirac String
    Masasi Fujigaki
  4. Progress of Theoretical Physics Vol. 53 No. 4 (1975) pp. 1162-1177 :
    Strong Interaction Property of Double Dirac String
    Masasi Fujigaki
  5. Progress of Theoretical Physics Vol. 54 No. 2 (1975) pp. 563-577 :
    Relativistic Mechanics of Two Interacting Particles and Bilocal Theory
    Takehiko Takabayasi
  6. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 210-228 :
    “Minimal Boosting” of SU(6) Scheme
    Shin Ishida, Azusa Matsuda and Mikio Namiki
  7. 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
  8. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 996-1008 :
    S-Matrix for Interacting Extended Boson Field. I
    A. Z. Capri and C. C. Chiang
  9. Progress of Theoretical Physics Vol. 59 No. 6 (1978) pp. 2121-2132 :
    Exceptional Waves and Characteristic Shocks on Non-Linear Relativistic Strings
    T. Ruggeri and A. Strumìa
  10. 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
  11. Progress of Theoretical Physics Vol. 60 No. 2 (1978) pp. 595-610 :
    Constituent Mass, Free-Limit Condition, and Quantization for Trilocal Theory
    Takehiko Takabayasi
  12. Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1235-1250 :
    Covariant Wave Equations of Two Spinning Particles Harmonically Bound
    Takehiko Takabayasi
  13. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1466-1476 :
    New Formalism for Simple Relativistic Oscillator Model and Electromagnetic Interaction
    Takehiko Takabayasi
  14. Progress of Theoretical Physics Supplement No.67 (1979) pp. 1-68 :
    Relativistic Mechanics of Confined Particles as Extended Model of Hadrons
    Takehiko Takabayasi
  15. Progress of Theoretical Physics Supplement No.86 (1986) pp. 81-92 :
    Theory of Relativistic String and Multilocal Model
    Takehiko Takabayasi

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