Prog. Theor. Phys. Vol. 52 No. 6 (1974) pp. 1953-1970

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

— Quantum-Field Theory of Non-Linear Realization and Current-Current Interaction of Pion Field —

Takao Okabayashi and Hiroyuki Kikugawa

Department of Physics, University of Tokyo, Tokyo

(Received February 12, 1974)

Abstract:

The purpose of the present article is twofold. First it is confirmed that the quantum-theoretical lagrangian formalism for quasi-linear field theories proposed in the first part of the present series of articles really reproduces all results in the quantum field theory of non-linear realization, which was settled by utilizing characteristic features of displacement operators in Minkowski space without referring to the lagrangian density operator in any aspect. The preferred field which appears in the field theory of non-linear realization is the simplest example of quasi-linear fields of the first class. Secondly, the formalism is applied to a realistic example of quasi-linear fields of the second class, in which pion field φ_α interacts with itself through the current-current interaction. Arbitrariness of the function Y of φ_α ², which is introduced to represent the arbitrariness of the order of operators in the definition of the quantum-theoretical `covariant' derivative, can be diminished to a large extent through the internal consistency of the formalism.

URL : http://ptp.ipap.jp/link?PTP/52/1953/
DOI : 10.1143/PTP.52.1953

References:

T. Okabayashi and H. Kikugawa, Prog. Theor. Phys. 52 (1974), 1687[PTP].
This article will be hereafter referred to as article I, and equations appearing in article I will be cited as Eq. (I·10b), for example.
Articles on other lagrangian formalisms of quasi-linear fields and on non-linear realization are listed up in article I.
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References 2), 3), 4) and 9) in the present article will be hereafter referred to as article A, B, C and D, respectively.
The metric and the choice of positive frequency part used in article A are different from in the present ones.
A few remarks on the content of article A are added in Appendices of this article.
T. Okabayashi, Prog. Theor. Phys. 50 (1973), 661[PTP]; ibid. 50 (1973), 1046[PTP].
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T. Okabayashi, T. Sasaki and K. Yoshikawa, Prog. Theor. Phys. 47 (1972), 293[PTP].
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Citing Article(s) :

Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1276-1287 :
Covariant Differential Operator under General Coordinate Transformation and Structure of Lagrangian Operator

Takao Okabayashi
Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 943-958 :
Local Gauge Invariance of Non-Abelian Gauge Field Theory

Takao Okabayashi and Norio Nakagawa
Progress of Theoretical Physics Vol. 61 No. 5 (1979) pp. 1499-1514 :
Quanta of Non-Abelian Gauge Field Can Be Transversal?

Takao Okabayashi
Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 201-213 :
T^*-Product Convention for Quasi-Linear Systems and for Transverse Non-Abelian Gauge Fields

Takao Okabayashi