---

Prog. Theor. Phys. Vol. 49 No. 4 (1973) pp. 1352-1361

Schwinger's Variation Principle by Means of Q-Number Variation for Non-Linear Lagrangian

Reiji Sugano

Department of Physics, Osaka City University, Osaka

(Received October 5, 1972)

Abstract:

Since the ordinary c-number variation principle does not lead, for a non-linear Lagrangian, to the result consistent between the Lagrangian and Hamiltonian formalisms, Schwinger's variation principle is reformulated for a type of Lagrangian L=½\dotqⁱg_ij(q)\dotq^j-u(q) by means of a q-number variation. The canonical momentum, the Hamiltonian, the canonical commutation relations and equation of motion are derived. Also the Euler-Lagrange equation is obtained, which is consistent with the canonical equation of motion. These consequences are exactly the same as those of previous papers, but different from the ordinary ones in the Euler-Lagrange equation and the Hamiltonian.

URL : http://ptp.ipap.jp/link?PTP/49/1352/
DOI : 10.1143/PTP.49.1352

[ Full Text PDF : FREE ACCESS (668K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. H. E. Lin, W. C. Lin and R. Sugano, Nucl. Phys. B 16 (1970), 431 [CrossRef]
2. R. Sugano, Prog. Theor. Phys. 46 (1971), 297[PTP].
3. 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].
4. J. Schwinger, Phys. Rev. 82 (1951), 914[APS].
5. J. Schwinger, Field Theory and Particles in Brandeis Lectures in Theoretical Physics, Vol. 2 (Prenticle Hall, Englewood Cliffs, New Jersey, 1964).
6. T. Kawai, Prog. Theor. Phys. 48 (1972), 2082[PTP]; Preprint of Osaka City University.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 50 No. 1 (1973) pp. 277-289 :

   Quantization for Non-Linear Lagrangian

   Teruya Ohtani

2. 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

3. Progress of Theoretical Physics Vol. 51 No. 2 (1974) pp. 592-599 :

   A Note on Covariant Derivatives in the Quantum Field Theory

   Takao Okabayashi

4. 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

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.