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.