GRMS or Graphical Representation of Model Spaces

GRMS or Graphical Representation of Model Spaces

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The purpose of these notes is to give some simple tools and pictures to physicists and ' chemists working on the many-body problem. Abstract thinking and seeing have much in common - we say qI seeq meaning qI understandq , for example. Most of us prefer to have a picture of an abstract object. The remarkable popularity of the Feynman diagrams, and other diagrammatic approaches to many-body problem derived thereof, may be partially due to this preference. Yet, paradoxically, the concept of a linear space, as fundamental to quantum physics as it is, has never been cast in a graphical form. We know that is a high-order contribution to a two-particle scattering process (this one invented by Cvitanovic(1984)) corresponding to a complicated matrix element. The lines in such diagrams are labeled by indices of single-particle states. When things get complicated at this level it should be good to take a global view from the perspective of the whole many-particle space. But how to visualize the space of all many-particle states ? Methods of such visualization or graphical representation of the , spaces of interest to physicists and chemists are the main topic of this work.By analogy to M-diagrams I will also use the name, S-diagram for branching diagram. The theory of groups gives two other ways of labeling the spin functions: U(n) group theory using Gelfand tableaux, and SN group theory using Young tableaux. Both methods are ... 2 2 1 1 2S 7 1 0 2. Part I. Architecture of model spaces 45.

Title:GRMS or Graphical Representation of Model Spaces
Author:Wlodzislaw Duch
Publisher:Springer Science & Business Media - 2012-12-06


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