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Prog. Theor. Phys. Vol. 50 No. 5 (1973) pp. 1715-1728

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Q-Number Variational Method for Non-Linear Lagrangian in Quantum Mechanics

Teruya Ohtani and Reiji Sugano

Department of Physics, Osaka City University, Osaka

(Received June 14, 1973)

Abstract:

A previous q-number variational method is extended to be applicable to any quantum system for which the classical Lagrangian is given by Lc=½gij\dotqi\dotqj+ui\dotqi-v. The q-number variation is necessary for the formulation to be form-invariant under a general space-time transformation. From the action principle, not only the Euler-Lagrange equation but also the commutation relations up to a constant factor are obtained. Futhermore the form of the quantum Lagrangian is, to some extent, decided in order for solutions to exist for the action principle. It is shown that the first Noether theorem holds and the quantization is consistent with the canonical formalism.


URL : http://ptp.ipap.jp/link?PTP/50/1715/
DOI : 10.1143/PTP.50.1715

[ Full Text PDF : FREE ACCESS (974K) ] Citation:

References:

  1. R. Sugano, Prog. Theor. Phys. 46 (1971), 297[PTP].
    T. Kimura and R. Sugano, Prog. Theor. Phys. 47 (1972), 1004[PTP].
    T. Kimura, T. Ohtani and R. Sugano, Prog. Theor. Phys. 48 (1972), 1395[PTP].
  2. T. Ohtani and R. Sugano, Prog. Theor. Phys. 47 (1972), 1704[PTP].
  3. T. Ohtani, Prog. Theor. Phys. 50 (1973), 277[PTP].
  4. H. Kamo and T. Kawai, Prog. Theor. Phys. 50 (1973), 680[PTP].
  5. J. Schwinger, Field Theory and Particles in Brandeis Lectures in Theoretical Physics, Vol 2 (Prentice Hall, Englewood Cliffs, New Jersey, 1964), p. 150.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1769-1771 :
    Note on Quantum Form of Non-Linear Lagrangian
    Toshiei Kimura
  2. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1687-1701 :
    A Quantum-Theoretical Lagrangian Formalism for Quasi-Linear Field Theories. I
    Takao Okabayashi and Hiroyuki Kikugawa
  3. Progress of Theoretical Physics Vol. 58 No. 6 (1977) pp. 1964-1972 :
    On the Path Integral in the Curved Space
    Toshiei Kimura
  4. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1827-1842 :
    Quantum Theory of Massive Yang-Mills Fields. I
    Takashi Fukuda, Minoru Monda, Minoru Takeda and Kan-ichi Yokoyama
  5. Progress of Theoretical Physics Supplement No.109 (1992) pp. 1-17 :
    Chapter I. Quantization of Chiral Solitons in Collective-Coordinate Approach
    Kanji Fujii and Naohisa Ogawa

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