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Prog. Theor. Phys. Vol. 25 No. 5 (1961) pp. 803-821

[ Full Text PDF : FREE ACCESS (1063K) ]

Exact Treatment of the Bound State Problems in the Non-Relativistic Quantum Field Theory

Nobumichi Mugibayashi

Department of Physics, Kobe University, Kobe

(Received January 21, 1961)

Abstract:

An exact equation for the bound state of nucleons in the static neutral scalar moel is obtained by using the field equation for Heisenberg operator and the method of canonical transformation. The formulation of the eigenvalue problem is completed by the analyticity consideration. In particular, a boundary condition at τ=0 (-iτ being the “negative imaginary” relative time) turns out that the derivative of the “wave function” with respect to τ must be zero at τ=0. The abnormal solutions exist in this case as well as in the ladder approximation, but there is difference in nature between them for the zero meson mass case. The appearance of abnormal solutions is mainly due to the structure of the fundamental equation itself. This is demonstrated by handling a first order equation for the static neutral scalar model and the Bethe-Salpeter equation for the Lee model, in both cases of which the abnormal solutions do not appear.


URL : http://ptp.ipap.jp/link?PTP/25/803/
DOI : 10.1143/PTP.25.803

[ Full Text PDF : FREE ACCESS (1063K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 26 No. 1 (1961) pp. 99-122 :
    Some Converging Examples of the Perturbation Series in the Quantum Field Theory
    Yusuke Kato
  2. Progress of Theoretical Physics Vol. 26 No. 4 (1961) pp. 470-482 :
    On Vertical Representation of Bethe-Salpeter Amplitudes
    Masakuni Ida and Kazumi Maki
  3. Progress of Theoretical Physics Vol. 92 No. 4 (1994) pp. 863-879 :
    Effective Action and Quantum Mechanics
    Kenji Shiraishi and Reijiro Fukuda
  4. Progress of Theoretical Physics Supplement No.121 (1995) pp. 1-428 :
    Novel Use of Legendre Transformation in Field Theory and Many Particle Systems
    Reijiro Fukuda, Masahiro Komachiya, Satoshi Yokojima, Yoko Suzuki, Ko Okumura and Takeshi Inagaki

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