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Prog. Theor. Phys. Vol. 42 No. 3 (1969) pp. 581-599

[ Full Text PDF : FREE ACCESS (844K) ]

On Collective Motion of Rotational Invariant System Composed of N-Particles

Tetsuo Gotō

Department of Physics and Atomic Energy Research Institute, Nihon University, Kanda-Surugadai, Chiyoda-ku, Tokyo

(Received April 14, 1969)

Abstract:

We study collective coordinates of rotational motion by means of canonical transformation. It is shown that our Hamiltonian is equivalent to that of Tamura, Nataf and Villars [T. Tamura, Nuovo Cim. 4 (1956), 1307; R. S. Nataf, Nucl. Phys. 2 (1957), 497; F. Villars, Annual Review of Nuclear Science (Annual Review Inc.) Vol. 7 (1957), p. 185]. Further investigation is carried out and it shows that a rotation-like collective motion is introduced besides rotation as a whole of a system and even in a spherically symmetric case we have rotational levels. Our interest is focussed on collective momenta rather than collective coordinates and they are generators of GL(3).


URL : http://ptp.ipap.jp/link?PTP/42/581/
DOI : 10.1143/PTP.42.581

[ Full Text PDF : FREE ACCESS (844K) ] Citation:

References:

  1. T. Tamura, Nuovo Cim. 4 (1956), 1307.
    R. S. Nataf, Nucl. Phys. 2 (1957), 497[CrossRef].
    F. Villars, Annual Review of Nuclear Science (Annual Review INC), Vol. 7 (1957), p. 185.
  2. A. Bohr, Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd 26 (1952), No. 14.
    A. Bohr and B. R. Mottelson, Danske Videnskab. Selskab, Mat.-fys. Medd 27 (1953), No. 16.
  3. See a review article by Villars in reference 1).
  4. P. A. M. Dirac, Lecture on Quantum Mechanics (Belfer Graduate School of Science, Yeshiva University, New York, 1964).
  5. Method used here is very similar to Tomonaga's method. S. Tomonaga, Prog. Theor. Phys. 13 (1955), 467[PTP]; ibid. 13 (1955), 482[PTP].
  6. O. Hara and T. Gotō, Prog. Theor. Phys. Suppl. No. 41 (1968), 56, [PTP]§13.
  7. K. Ikeda, M. Kobayasi and T. Marumori, Prog. Theor. Phys. 20 (1958), 460[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1973-1983 :
    Poincaré Group and the Relativistic Wave Equation of the Extended Particle Model
    Tetsuo Gotō

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