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Title: Unified theory of effective interaction

Abstract

We present a unified description of effective interaction theories in both algebraic and graphic representations. In our previous work, we have presented the Rayleigh–Schrödinger and Bloch perturbation theories in a unified fashion by introducing the main frame expansion of the effective interaction. In this work, we start also from the main frame expansion, and present various nonperturbative theories in a coherent manner, which include generalizations of the Brandow, Brillouin–Wigner, and Bloch–Horowitz theories on the formal side, and the extended Krenciglowa–Kuo and the extended Lee–Suzuki methods on the practical side. We thus establish a coherent and comprehensive description of both perturbative and nonperturbative theories on the basis of the main frame expansion.

Authors:
Publication Date:
OSTI Identifier:
22617369
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTURBANCES; PERTURBATION THEORY; QUANTUM MECHANICS

Citation Formats

Takayanagi, Kazuo, E-mail: k-takaya@sophia.ac.jp. Unified theory of effective interaction. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.04.011.
Takayanagi, Kazuo, E-mail: k-takaya@sophia.ac.jp. Unified theory of effective interaction. United States. doi:10.1016/J.AOP.2016.04.011.
Takayanagi, Kazuo, E-mail: k-takaya@sophia.ac.jp. 2016. "Unified theory of effective interaction". United States. doi:10.1016/J.AOP.2016.04.011.
@article{osti_22617369,
title = {Unified theory of effective interaction},
author = {Takayanagi, Kazuo, E-mail: k-takaya@sophia.ac.jp},
abstractNote = {We present a unified description of effective interaction theories in both algebraic and graphic representations. In our previous work, we have presented the Rayleigh–Schrödinger and Bloch perturbation theories in a unified fashion by introducing the main frame expansion of the effective interaction. In this work, we start also from the main frame expansion, and present various nonperturbative theories in a coherent manner, which include generalizations of the Brandow, Brillouin–Wigner, and Bloch–Horowitz theories on the formal side, and the extended Krenciglowa–Kuo and the extended Lee–Suzuki methods on the practical side. We thus establish a coherent and comprehensive description of both perturbative and nonperturbative theories on the basis of the main frame expansion.},
doi = {10.1016/J.AOP.2016.04.011},
journal = {Annals of Physics},
number = ,
volume = 372,
place = {United States},
year = 2016,
month = 9
}
  • We present a unified description of the Bloch and Rayleigh–Schrödinger perturbation theories of the effective interaction in both algebraic and graphic representations.
  • We present a unified effective field theory for the light mesons and heavy mesons which integrates many features from the quark model, vector dominance, chiral dynamics, Skyrmion physics, and the heavy quark effective theory into a single universal theory. By identifying the meson fields as the Bargmann-Wigner superfields with the direct product representation of a quark and antiquark and using the Bargmann-Wigner equation and Lagrangian, we can readily match the meson Lagrangian with the quark Lagrangian. Thus we not only incorporate various aspects of the quark contents into the meson fields but we can also transcribe the implementation of themore » chiral symmetry and spontaneous symmetry breakings from the quark Lagrangian to the meson Lagrangian. The physical light meson fields can be constructed nonlinearly from the quark and antiquark direct product representation, with the 0{sup {minus}} pseudoscalar mesons as the Goldstone mesons and the 1{sup {minus}} vector mesons as the non-Abelian gauge fields of the hidden local SU(3) symmetry. Phenomenological consequences and theoretical implications of this theory will be discussed. Various aspects of the heavy quark effective theory are automatically integrated into this formulation. {copyright} {ital 1997} {ital The American Physical Society}« less
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