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Prog. Theor. Phys. Vol. 45 No. 1 (1971) pp. 251-262

Currents in the Non-Linear Realization of a Group on Its Sub-Group

Takao Okabayashi

Department of Physics, University of Tokyo, Tokyo

(Received August 3, 1970)

Abstract:

In the non-linear realization of a group on its sub-group, there is a method to define currents which can be classified between the Lagrangian formalism and the local current algebra in respect of the model dependence. In addition to the minimum condition that a current should be a base vector of a linear adjoint representation, some additional requirements which depend on models very loosely are imposed. Then the current can be defined uniquely without any reference to the equations of motion of the constituent fields, and the types of the symmetry violation and the models are restricted. The violation should be additive in the language of Lagrangian formalism, and the field-current identity hypothesis, for example, is not applicable to the non-linear realization. Furthermore there is no quantization method which is consistent with the local current algebra.

URL : http://ptp.ipap.jp/link?PTP/45/251/
DOI : 10.1143/PTP.45.251

[ Full Text PDF : FREE ACCESS (691K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. See, for instance, S. L. Adler and R. F. Dashen, Current Algebras (W. A. Benjamin, Inc., New York, 1968).
2. R. P. Feynman, M. Gell-Mann and G. Zweig, Phys. Rev. Lett. 13 (1964), 678[APS].
3. R. Dashen and M. Gell-Mann, Phys. Rev. Lett. 17 (1966), 340[APS].
4. T. Okabayashi and T. Watanabe, Prog. Theor. Phys. 43 (1970), 1085[PTP]; ibid. 43 (1970), 1343[PTP].
   This article will be referred in the following as article I. Earlier references about the non-linear realization will be found in this article.
5. E. Cartan, Leçons sur la théorie des spineurs (Hermann, Paris, 1938).
6. S. Weinberg, Phys. Rev. 166 (1968), 1568[APS].
7. T. Okabayashi and T. Watanabe, Prog. Theor. Phys. 45 (1971), 243[PTP].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 46 No. 2 (1971) pp. 634-658 :

   A Quantum Theory of the Non-Linear Realization of a Group on Its Sub-Group

   Takao Okabayashi

2. Progress of Theoretical Physics Vol. 47 No. 4 (1972) pp. 1343-1366 :

   A Model for the Broken SU(3) Symmetry Based on the Non-Linear Realization of the Group

   Takao Okabayashi

3. Progress of Theoretical Physics Vol. 48 No. 4 (1972) pp. 1375-1394 :

   An Ambiguity in Particle Interpretation of Gauge Field of the Yang-Mills Type

   Takao Okabayashi

4. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 661-679 :

   A Quantum Theory of a Conjugate Pair of Preferred Fields Interacting with a Spinor Field. I

   Takao Okabayashi

5. Progress of Theoretical Physics Vol. 52 No. 6 (1974) pp. 1953-1970 :

   A Quantum-Theoretical Lagrangian Formalism for Quasi-Linear Field Theories. II

   Takao Okabayashi and Hiroyuki Kikugawa

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