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Afterword

Published online by Cambridge University Press:  12 January 2010

Yoshio Kuramoto
Affiliation:
Tohoku University, Japan
Yusuke Kato
Affiliation:
University of Tokyo
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Summary

We have discussed the physical and mathematical aspects of one-dimensional quantum particles with1/r2 interactions. On the physics side, we began with the simplest two-body system, and culminated in the exact dynamics of a supersymmetric electronic model. In this way we have tried to draw a comprehensive picture of one-dimensional quantum systems, taking the canonical systems with 1/r2 interactions. On the mathematical side, the most important subjects are first the Jack polynomials, and second the Yangians. These two subjects were originally developed independently, but are actually closely interrelated. Our basic viewpoint is that the 1/r2 systems provide the most natural working model to synthesize these two subjects, and to sharpen the concepts further.

There are many topics, however, which we could not discuss in this book. This is firstly because of our insufficient understanding of the topics, and secondly because of our intention of making a reasonably sized book. We shall mention some of the omitted topics, hoping that they will be covered on another occasion.

Examples of other canonical systems, which have escaped our discussion in this book, include the Calogero–Sutherland model with harmonic confinement. The spectrum of the model is equidistant as in the simple harmonic oscillator. Because of this feature the model can be compared with the chiral conformal field theory (CFT) with right-going particles only. We refer to a recent review [88] for the systems. In relation to the CFT, there are active studies to investigate the quasi-particle structure for the general case of the internal symmetry.

Type
Chapter
Information
Dynamics of One-Dimensional Quantum Systems
Inverse-Square Interaction Models
, pp. 455 - 457
Publisher: Cambridge University Press
Print publication year: 2009

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  • Afterword
  • Yoshio Kuramoto, Tohoku University, Japan, Yusuke Kato, University of Tokyo
  • Book: Dynamics of One-Dimensional Quantum Systems
  • Online publication: 12 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511596827.012
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  • Afterword
  • Yoshio Kuramoto, Tohoku University, Japan, Yusuke Kato, University of Tokyo
  • Book: Dynamics of One-Dimensional Quantum Systems
  • Online publication: 12 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511596827.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Afterword
  • Yoshio Kuramoto, Tohoku University, Japan, Yusuke Kato, University of Tokyo
  • Book: Dynamics of One-Dimensional Quantum Systems
  • Online publication: 12 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511596827.012
Available formats
×