Prog. Theor. Phys. Vol. 50 No. 1 (1973) pp. 277-289

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Quantization for Non-Linear Lagrangian

— Cases of Point Mechanics and Scalar Field —

Teruya Ohtani

Department of Physics, Osaka City University, Osaka

(Received January 16, 1973)

Abstract:

The quantization for non-linear Lagrangian
L=(1/8) g^-1/4{g_jk,\dotq^k}g^1/2g^ij{g_il,\dotq^l}g^-1/4-v(q)
is examined. It is shown that the variational method, which was formulated in previous papers, may be applicable only to the case with constant curvature. In the case of constant curvature, the first Noether theorem can be extended to the quantum theory. The quantization of point mechanics is extended to that of a scalar field. And the conservation law corresponding to the inhomogeneous Lorentz transformation is obtained.

URL : http://ptp.ipap.jp/link?PTP/50/277/
DOI : 10.1143/PTP.50.277

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Citing Article(s) :

Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 680-690 :
Schwinger's Variational Principle in Quantum Mechanics with Velocity Dependent Potential. III

Hideki Kamo and Toshiharu Kawai
Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1715-1728 :
Q-Number Variational Method for Non-Linear Lagrangian in Quantum Mechanics

Teruya Ohtani and Reiji Sugano
Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1769-1771 :
Note on Quantum Form of Non-Linear Lagrangian

Toshiei Kimura