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Prog. Theor. Phys. Vol. 12 No. 1 (1954) pp. 94-98

[ Full Text PDF : FREE ACCESS (303K) ]

On the Effective Hamiltonian for Pseudoscalar Meson with Pseudoscalar Coupling with Nucleon

Tomoya Akiba and Katuro Sawada*

Department of Physics, Tohoku University
*Tokyo University

(Received April 15, 1954)

Abstract:

The method of canonical transformation is applied to the pseudo-scalar meson theory with pseudoscalar coupling. It well be shown that the Tani-Foldy transformation results as the best one when regarded as a variational function among the similar family of transformation. The resulting Hamiltonian was ordered assuming some cut-off for the virtual meson momentum, and performing the mass renormalization. This Hamiltonian shows a good tendency to account for the S-phase shifts for the nucleon π-meson scattering; the L-S coupling (τ·φ×π) in the isotopic spin space, which is positive for the T=3/2 state and negative for the T=1/2 state, becomes twice as large as obtained by the perturbation theory.


URL : http://ptp.ipap.jp/link?PTP/12/94/
DOI : 10.1143/PTP.12.94

[ Full Text PDF : FREE ACCESS (303K) ] Citation:

References:

  1. S. Tani, Prog. Theor. Phys. 6 (1950), 267[PTP].
  2. L. L. Foldy, Wouthuysen, Phys. Rev. 78 (1950), 29[APS].
  3. The similar effective Hamiltonian for the Dyson transformation was obtained by
    S. D. Drell and E. M. Henley, Phys. Rev. 88 (1952), 1053[APS].
  4. We take natural units, c=1, \hbar=1.
  5. Here we take, for simplicity, as arguments of the function f, the form (φ2)v2.
  6. The expression π·f(φ) mesons ½{π,f(φ)}+ and its vacuum expectation value <½{π, f(φ)}+>=0.
  7. <φ2>0 means <φi2>0 with i any one of 1, 2, 3, φ2=φ12+φ22+φ32..

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 12 No. 5 (1954) pp. 689-691 :
    A Generalization of the Foldy Transformation in Ps-Ps Meson Theory
    Pong Yul Pac, Smio Tani and Kazuo Yamazaki
  2. Progress of Theoretical Physics Vol. 12 No. 6 (1954) pp. 723-746 :
    On the Meaning of the Solution of the One-Body Dirac Equation
    Smio Tani and Kazuo Yamazaki
  3. Progress of Theoretical Physics Vol. 12 No. 6 (1954) pp. 767-788 :
    Pion-Nucleon Scattering in the Tamm-Dancoff Approximation
    Shin Chiba, Miwae Yamazaki and Nobuyuki Fukuda
  4. Progress of Theoretical Physics Vol. 13 No. 6 (1955) pp. 594-602 :
    On the Intermediate Coupling Theory of Pseudo-Scalar Meson Field and a Nucleon
    Daisuke Ito, Yoneji Miyamoto and Yukihiko Watanabe
  5. Progress of Theoretical Physics Vol. 17 No. 4 (1957) pp. 581-591 :
    Pion-Nucleon Scattering and Structure of Fourth-Order Matrix Elements in Ps(Ps) Meson Theory
    Kugao Nakabayasi and Kazu Hasegawa
  6. Progress of Theoretical Physics Vol. 18 No. 4 (1957) pp. 383-395 :
    Static Model in the Meson Theory
    Masao Sugawara
  7. Progress of Theoretical Physics Vol. 19 No. 3 (1958) pp. 330-338 :
    On the Static Approximation of the γ5 Meson Theory
    Akira Kanazawa
  8. Progress of Theoretical Physics Vol. 20 No. 2 (1958) pp. 149-162 :
    Electromagnetic Properties of Nucleons
    Akira Kanazawa, Shinya Furui and Tetsuro Sakuma
  9. Progress of Theoretical Physics Vol. 20 No. 2 (1958) pp. 216-238 :
    Effects of Virtual Nucleon Pairs to the Electromagnetic Structure of the Nucleon
    Shigeo Goto and Shigeru Machida
  10. Progress of Theoretical Physics Vol. 20 No. 4 (1958) pp. 487-504 :
    Effect of the Non-relativistic Recoil of a Source Particle in Quantum Field Theories
    Jun'ichi Osada and Haruyuki Fujino
  11. Progress of Theoretical Physics Vol. 22 No. 3 (1959) pp. 381-395 :
    Pseudoscalar Coupling and S-Wave Pion-Nucleon and Kaon-Nucleon Scattering
    Reiji Sugano
  12. Progress of Theoretical Physics Vol. 23 No. 6 (1960) pp. 1216-1218 :
    The Effect of π2 Term in the S-Wave π-N Scattering
    Isao Umemura
  13. Progress of Theoretical Physics Vol. 77 No. 3 (1987) pp. 502-507 :
    A Variational Approach to Chiral Quark Models
    Yasuhiko Futami, Yasuhiko Odajima and Akira Suzuki
  14. Progress of Theoretical Physics Vol. 84 No. 3 (1990) pp. 377-380 :
    The Nonlinear Effects of Pion-Quark Coupling in the Cloudy Bag Model
    Yasuhiko Futami and Satoru Akiyama

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